'•*^- 


^^-^^^ 


.e^2^ 


NOTICE 


This  Book  is  the  Property  of 

AUG.  S.  BURGESS 

/^nd  whoever  borrows  the  same 

is  requested  not  to  lend  at  to 
any  individual,  take  particular 
pains  to  keep  it  clean,  and  not 
lurn  the  corners  of  the  leaves 
down,  or  deface  it  whatever. 
AUG.    S.   BUEGESS. 

N  B.  A  borrowed  book  should 
be  returned  as  good  as  when 
taken.— A.  S.  B. 


UCSB   LIBRARY 


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PEOPLES' 

POCK[T  STl  BUILDER 


-ANl 


Carpenters'  Hand  Book. 


CONTAINING  FIFTY- ONE  PLATES.  AND   OVER 

FIVE  HUNDRED  FIGURES,   WITH  A  FULL 

DESCRIPTION  FOR  EVERY  FIGURE. 


EMBRACING 

Carpenters'  and  Stalr-Bnllders'  Geometry,  Problems,  Conic 
Sections,  CyllndLric  Keetlons,  as  applied  in  tbe  construction 
of  tbe  Wreatb  part  of  Hand-rail.  Rales  for  tbe  Measure- 
ment of  Surfaces.  Tbe  Construction  of  I^adders,  Box  Stairs, 
Dog-legg:ed,  Open  Newel,  Cylinder,  Circular  and  Elliptical 
Staircases. 

ROOFING— Hip,  Talley,  and  Jack  Rafters.  PurUns,  Splayed 
Work,  and  Bevels  for  tbe  same.  Transverse  Strengrtb  of 
Joist  and  Beams,  and  easy  formulas  for  tbeir  safe  load. 

ALSO, 
Excavators,  Stone  and  Brick  Masons,  Plasterers  and  Carpen- 
ters' Memoranda ;  witb  a  variety  of  miscellaneous  informa- 
tion, useful  in  tbe  practice  of  tbe  Arcbltect  and  Builder; 
to^etber  witb  a  Glossary  of  Arcbitectural  Terms,  and 
General  Index. 


By   WILLIAM    PEOPLES. 


David  Williams  Company,  Publishers,  232-238  William  St., 
New  York. 


PREFACE. 


For  some  jears  it  has  been  the  aim  of  tlie  author  to  prepare 
a  small  book  for  the  young  stair  builder-,  carpenter  and  joiner, 
as  a  handy  reference,  that  ^vould  be  to  them  what  Has  well  and 
Trautwine  are  to  the  engineer.  Having  now  worked  at  the  trade 
of  carpentry  and  stair-bniiding  48  years,  the  author  is  free  to  say 
from  experience,  that  a  little  book  of  this  kind  for  the  pocket 
is  a  much  needed  acquisition  for  the  benefit  of  the  apprentice 
and  journeyman  as  well. 

So  much  has  been  sai^l  on  the  subject  that  it  is  next  to 
impossible  to  be  wholly  original,  and  no  claim  of  that  nature  is 
preferred.  It  is  simply  an  arrangement  of  ideas,  gleaned  from 
the  various  work  of  authorities,  and  modified  by  the  author's 
practice,  embodied  in  book  form. 

If  this  little  volume  should  lead  the  student  of  carpentry 
and  stair-building  to  study  the  suljject  carefully,  and  be  induced 
to  practice  the  same  with  pleasure  and  profit  to  himself,  the 
author  will  be  satisfied  that  his  efforts  liave  not  been  in  vain. 

The  young  man  should  provide  himself  with  a  drawing 
l)oard,  say  fi4''  l>y  '.jiV^  and  JX'^  thick,  with  two  battens  across 
the  back  to  keep  the  board  true;  joint  tlie  same  square  and 
straight,  and  to  a  parallel  width.  Provide  a  .set  of  draughting 
inrtruments,  T  square  about  3'  long,  and  two  triangles,  one 
45°  and  the  other  60°,  a  dozen  thumb  tacks,  a  6-H  pencil  and 
rubber.  Use  India  ink  for  inking.  Tlie  instruments  can  all  be 
bought  separately,  and  if  the  young  man  cannot  afford  to 
))urcliase  a  full  set  of  good  tools,  then  buy  one  at  a  time,  for  one 
good  tool  is  worth  more  than  a  chest  full  of  ba<l  ones. 

Tiie  apprentice  should  study  these  jilates  one  at  a  time, 
by  drawing  each  figure  to  a  larger  scale,  either  quarter,  half  or 
full  size;  let  all  leisure  time  be  applied  in  this  way,  and  if 
persevered  in.  the  success  of  the  young  man  is  as  sure  as  the  sun 
shines  or  the  earth  moves. 

Peter  Nicholson's  schooling  was  very  limited  Coiily  three 
years)  eiuling  at  twelve,  and  yet  by  persevering  industry  he 
mastered  the  higher  branches  of  mathematics,  and  produced  the 
"Carpenters  Ouide."  tliat  was  for  half  a  century  the  carpenters 
and  joiners  palladium.  Then  let  not  the  young  man  get  dis- 
couraged, but  iiitply  his  mind  anil  his  heart  to  his  trade,  studying 
the  same  in  all  its  liranches,  first  the  rudiments  or  first  prin- 
ciples, then  the  higher  branches;  if  so.  he  cannot  fail  of  attain- 
ing the  highest  skill,  and  demanding  tlie  best  wages. 

aiind,  there  is  no  royal  road  to  this  end;  all  spare  time  from 
his  regular  duties  should  be  apj)lied  at  the  draught-board  and 
his  books,  while  serving  his  ap])renticeship.  What  is  true  of 
Jlr.  Nicholson  is  also  true  of  hundreds  of  other  self-made  men; 
ami  yet  at,  or  near  tlie  end  of  tlie  nineteenth  century,  when 
many  are  running  to  and  fro  and  knowledge  is  being  increased, 
when  mechanics  and  professions  are  opening  their  store  houses 
of  knowledge  and  scattering  it  to  the  four  winds,  through  the 


4  Preface, 

press  and  other  avenues  the  ycmng  man  of  to-day  lias  a  conipaia- 
tively  easy  task  over  those  who  have  gone  before. 

Tlie  autlior  recommends  tlie  study  of  the  prismatic  solid  in 
connection  with  his  drawing,  as  the  best  means  to  gain  a 
tliorough  linowledge  of  hand-railing;  for  in  the  solid  the  reason 
for  every  line  may  be  more  easily  understood.  The  use  of  the 
trannnel  is  also  recommended  to  trace  the  curves  of  face-mould 
for  all  platform  and  level  landing  cylinders  up  to  24^'  diameter 
and  all  over  that  diameter  and  for  winders,  where  the  mould 
is  increased  in  length,  the  bisection  of  the  chord  and  use 
of  ordinates  is  found  to  be  the  most  simple  and  convenient 
method  to  find  the  trace  of  the  mould.  This,  the  author  believes, 
is  the  first  time  this  method  has  been  reconnuended  in  a 
general  way. 

Proving  the  angle  of  tangf^nts  on  the  face-mould  is  also 
recommended:  for  if  the  parallelogram  be  incorrect  on  the 
diagonal  or  chord,  the  joints  of  wreath  piece  will  be  incorrect, 
and  the  result  a  bad  piece  of  work. 

The  manner  of  taking  the  dimensions  in  the  building  and 
trimming  the  well,  together  with  instructions  in  laying  out  the 
stairs  and  preparing  them  at  the '  bench  ready  to  put  up,  is 
explained,  so  that  the  young  man  with  a  little  study  and  practice 
may  soon  learn  to  do  the  work.  Also  the  method  of  taking 
the  lengths  of  straight  rail,  from  the  stairs,  when  stepped  up, 
and  joiiding  and  dressing  the  rail  at  the  bencli  ready  to  be  set 
up  in  the  building,  is  shown  and  recouunended  as  the  best  and 
most  economical. 

The  carpenter  and  joiner  will  find  some  useful  information 
in  framing  hip  and  valley  rafters  and  bevels  for  the  same,  and 
also  a  method  to  find  the  l)evels  for  any  kind  of  splayed  work; 
also  formulas  for  the  strength  of  joist  and  their  safe  load. 

A  brief  history  of  stair  Iniilding  is  also  added,  together  with 
a  list  of  nearly  all  the  different  authors  that  have  written  on  the 
subject  in  our  language,  which  the  author  believes  will  be 
interesting  to  the  stair-builder. 

A  glossary  of  terms  and  an  index  is  also  added  to  make  the 
book  complete. 

The  Autiiok. 


CONTENTS. 

Comprising  in  all  the  different  Plates,  510  Fioures. 


PIRATE  1.  E.xliibits  the  Cui-penlcis,  Joiners  and  SI  air  Builders' 
Geometry. 

PI.ATE  2.    Exhibits  the  Circle  and  Graphical  Troblenis. 

PtATE  3.    Exhibits  Graphical  Problems  in  Geometry. 

PLATE  4.  Exhibits  the  Cone,  and  liow  to  prepare  a  templet  for 
the  turner  to  turn  a  Circular  Moulding  tliat  \s'ill  member  witli 
tlie  Common  Moulding  on  a  given  miter. 

PLATE  5.  Exliibits  the  Ellip.se,  and  diiferent  methods  of  con- 
structing the  .same. 

PLATE  6.  Exhibit.s  the  Scroll,  and  how  to  construct  the  .same; 
also  to  prepare  a  templet  for  the  turner  to  turn  a  cap  tliat  will 
member  witli  tlie  straight  rail  on  a  given  miter. 

PLATE  7.  Exhibits  the  construction  of  a  Face-mould  for  a  Wreath- 
piece  over  a  quarter  circle  on  plan,  having  a  full  easing.  ALso 
showing  the  principle  by  prismatic  solids  in  isonietrlcal  pro- 
jection; and  how  to  slide  the  mould. 

PLATE  8.  Exhibits  the  construction  of  a  Face-mould  for  a  Wreath- 
piece  over  a  quarter  circle  on  plan,  liaving  an  intermediate 
easing.  Tlie  principle  also  illustrated  by  the  triangular  prisms 
in  isometrical  projection;  also  how  to  slide  tlie  mould. 

PLATE  9.  Exhibits  the  construction  of  a  Face-mould  for  a  Wreath- 
piece  over  a  quarter  circle  on  plan,  without  an  easing.  Illus- 
trated same  as  for  plate  8. 

PLATE  10.  Exhibits  the  construction  of  a  Face-mould  for  a 
Wreath-piece  having  a  full  easing,  over  a  plan  less  than  a  quarter 
circle.  The  .sliding  of  the  mould,  aiul  the  principle  illustrated, 
same  as  for  plate  7. 

PLATE  11.  Exhibits  the  construction  of  the  Face-mould  for  a 
Wieatli-piece  having  an  intermediate  easing,  over  a  plan  less 
than  a  quarter  circle,  the  sliding  of  the  mould.  Also  the  prin- 
ciple illustrated  by  the  system  of  triangular  prisms. 

PLATE  12.  Exhil)its  the  construction  of  the  Face-mould  for  a 
Wreath-piece  without  an  easing,  over  a  plan  less  than  a  quarter 
circle.  The  sliding  of  the  mould,  and  the  triangular  prisms 
illustrated  in  isometrical  projection. 

PLATE  13.  Exhibits  the  construction  of  the  Face-mould  for  a 
Wreath-piece  over  a  plan  greater  than  a  quarter  circle,  for  three 
kinds  of  moulds. 

PI'ATE  1-1.  Exhibits  the  construction  of  a  Face-mould  for  a 
Wreath-piece  that  is  elliptical  on  plan,  and  less  than  a  quarter 
of  an  ellipsis. 


6  Contents. 

PIRATE  15.  Exliiljits  how  to  place  the  risers  in  a  semi  and  quarter 
cylinder  so  as  to  construct  the  wreath-piece  from  the  least 
thickness  of  stuff. 

PIRATE  16.  Exhibits  how  to  place  the  risers  in  a  cylinder  at  the 
startings  and  landings  of  a  flight  of  stairs,  so  lliat  one  mould 
will  answer  for  both. 

PIRATE  17.  Exhibits  the  construction  of  the  Face-mould  over  a 
quai'ter  cylinder,  to  obtain  the  wreath-piece  from  the  least  thick- 
ness of  stuff.    Also  the  face-mould  for  a  turnout  at  the  newel. 

PLATE  18.  Exhibits  the  construction  of  Box  Stairs  and  steps  to 
cellar  and  to  the  roof.  Also  the  steps  at  the  front  door  of  a 
residence. 

PEATE  19.    Exhibits  the  construction  of  Box  Stairs. 

PEATE  20.  Exhibits  the  construction  of  Box  Stairs  tliat  are 
winding. 

PEATE  21.  Exhibits  the  const  ruction  of  a  Wall-riul  for  a  Box  Stairs 
winding  at  the  starting. 

PEATE  22.  Exhibits  the  construction  for  a  Half-pace  Stair-case 
for  a  six  foot  hall,  and  seven  inch  cylinder  with  detail  for  same. 

PEATE  23.  A  continuation  of  the  detail.  Also  the  construction  of 
the  bearer  underneath  tlie  stairs,  so  as  not  to  deflect  .03  of  an 
inch  per  foot  in  length. 

PEATE  24.  Exhibits  the  construction  of  the  Face-moulds  and  other 
patterns  for  the  Stair-case,  plate  22.    Also  the  .sliding  of  the  mould. 

PEATE  25.  Exhibits  the  construction  of  a  Two-story  Stair-case 
for  a  hall  8  feet  2  inches  wide,  and  12  inch  cylinder. 

PEATE  26.  Exhibits  the  detail,  .showing  how  to  form  tlie  wall  and 
outer  strings,  also  lay  out  the  cylinders  for  the  same,  and  for  tlie 
turnout  at  the  newel. 

PE.\TE  27.  A  continuation  of  the  details  for  the  stair-case,  plate 
2.'),  .showing  the  .setting  of  newel,  length  of  staves,  and  cut  of 
cylinders. 

PE.\TE  28.  Exhil)its  the  construction  of  a  Veneered  String  around 
the  cylinder  by  bending  over  a  drum.  Also  how  to  construct  the 
face-mould  and  wreath  piece  over  winders  in  a  quarter  cylinder, 
and  work  the  ramp  at  the  lower  end,  in  the  shank  of  wreath- 
piece. 

PliATE  29.  Exhibits  the  construction  of  Face-moulds  and  easing 
patterns  required  for  the  stair-case,  plate  25. 

PEATE  30.  Exhibits  the  construction  of  Face-mould  for  the 
wicatli-rail  for  a  12  inch  cylinder  when  the  risers  are  placed  at 
any  point  in  the  cylinder,  or  may  be  misplaced  therein. 

PIjATE  31.  Exhibits  the  construction  of  a  One-«tory  Stair-case  in 
a  hall  10  feet  3  inches  wide,  having  a  24  inch  cylinder;  also  the 
detail  for  spacing  the  balusters  and  locating  the  risers  in  the 
same,  and  liow  to  form  tlie  concave  and  convex  risers. 

I'EATE  32.  Exhibits  the  construction  of  Face-mould,  Bevels,  and 
application  for  the  wreath-rail,  plate  31. 

PEATE  33.  Exhibits  the  detail  and  Face-moulds  for  the  Plaster 
Moulding;  also  length  of  staves,  and  veneering  the  cylinder  for 
plate  31. 


Contents.  7 

PIRATE  34.  Exhibits  the  construction  of  a  Two-story  Stair-case 
of  mixed,  straight  and  winding  steps.  The  first  flight,  a  half- 
pace  winding;  and  the  second  flight,  a  double  quarter-pace 
winding.  Also  showing  detail  of  the  cylinders,  and  the  spacing  of 
staves,  balusters  and  risers  in  the  same,  and  how  to  space  the 
scantling  for  supporting  the  flights. 

PLATE  35.  Exhibits  the  detail  of  the  Outer  and  Wall  Strings  for 
the  first  flight,  plate  34. 

PI..ATE  36.  Exhibits  tlie  detail  of  the  Outer  and  Wall  Strings  for 
the  second  flight,  and  how  to  line  off  the  same  for  plate  'H. 

PliATE  37.  Exhibits  the  Face-moulds,  Ramps,  and  easing  patterns 
for  the  stair-case,  plate  34. 

PliATE  38.  Exhibits  a  One-story  Stair-case,  dou])le  quarter-pace 
winding  in  the  first  flight,  having  a  circular  wall  string  at  the 
starting;  also  detail  of  cylinders  sliowiug  how  to  space  off  the 
lialusters,  and  locate  the  risers  in  the  same.  Also  how  to  find  the 
curve  of  grounds  at  the  head  of  the  nitch  in  a  circular  wall. 

PLATE  39.  Exhibits  the  detail  of  Wall  and  Outer  Strings,  and 
how  to  line  off  the  same  for  the  stair-case,  plate  38. 

PLATE  40.  Exhibits  the  Face-moulds  and  Easing  Patterns  of  the 
hand-rail  for  the  stair-case,  plate  38. 

PLATE  41.  Exhibits  two  methods  how  to  draw  the  Face-mould 
for  a  hand-rail  over  a  quarter  circle  containing  winders,  and 
starting  from  a  newel  post. 

PLATE  42.  Exhibits  the  construction  of  a  Face-mould  over  a 
quarter  circle  on  plan  having  winders  in  the  same.  Also  how 
to  place  risers  in  a  half-pace  so  as  to  avoid  winders,  and  the 
face-moulds  and  ramp,  and  easing  patterns  for  the  same;  and 
how  to  place  the  carriages  for  supporting  the  stair-case. 

PL.%TE  43.  Exliibits  the  construction  of  Face-moulds  and  Ramp. 
Patterns  for  the  wreath-rail  in  three  pieces,  over  a  .semicircle  20 
inches  in  diameter,  and  containing  seven  risers;  also  the  face- 
moulds  and  ramp  patterns  over  a  cylinder  struck  from  two  centers 
and  landing  on  the  floor. 

PLATE  44.  The  construction  of  Face-moulds  for  the  Wreath-rail 
over  15  winders,  being  circular  on  plan;  also  the  manner  of 
hor.seing  up  the  same. 

PLATE  45.  The  construction  of  Face-moulds  for  the  Wreath-rail 
of  a  Stair-case  that  is  elliptical  on  plan,  and  containing  17  risers; 
also  the  placing  of  bearers  underneath. 

PLATE  46.  Exhiljits  fourteen  different  profiles  of  double  and 
single  hand-rails. 

PLATE  47.  Exhibits  the  construction  of  an  Open  Newel  Stair- 
case; the  manner  of  lining  off  the  newels,  connecting  the  rails 
and  strings  to  the  newels,  and  details  for  glueing  up  the  same. 

PLATE  48.  Exhibits  the  construction  of  a  Hip-roof;  how  to  find  the 
lengths  and  cuts  of  hip,  valley,  jack,  and  common  rafters;  and 
also  purlins,  two  methods  are  here  sliown. 

PLATE  49.  Exhibits  a  simple  method  liow  to  find  the  lengtli  of 
Hip  and  Jack-rafters;  the  angles  of  plan  being  acute  and  obtuse, 
and  also  the  cuts  for  the  same. 


8  Contents. 

PIRATE  50.  Exhibits  the  Cuts  for  Splayed  Jambs  or  Soffits,  either 
miter  or  butt-cut  in  the  angle,  or  inclining  posts  intersecting 
vertical  ones.  The  development  of  a  veneer  for  a  circular-shaped 
head,  or  soffit  of  a  circular  arch,  in  a  circular  wall,  or  the  curve 
for  a  circular  pew  back. 

PL,ATE  51.  Exliibits  liow  to  find  the  length  and  curve  for  Angle 
Brackets,  and  the  groin  and  jack  ribs  for  vaulting. 

MECIIAXICAIi  C'ARPEXTRY.  Showing  simple  methods  how  to 
calculate  the  bearing  strengtli  of  joist,  beams,  headers  struts, 
columns,  or  the  the  strain  they  may  be  subjected  to  from  a  given 
load;  and  how  to  find  the  required  dimension  of  timber  to  safely 
resist  the  given  load.  Also  tables  showing  the  weight  per  cubic 
foot  for  the  different  kinds  of  materials,  botli  for  constructing 
and  loading  of  buildings,  and  the  compressive,  tensile,  and  trans- 
verse strengtli  of  same  per  inch.  Also  memoranda  for  excava- 
tors, stone  and  brick  masons,  plasterers  and  carpenters;  and 
otlier  miscellaneous  information,  valuable  to  the  builder. 

OKXERAE  INDEX  and  Glossary  of  Architectural  terms,  gathered 
from  all  sources. 


History  of  Stair  Building. 


As  our  country  is  comparatively  new,  being  now  189:3,  only 
four  hundred  years  since  its  discovery  by  Christopher  Columbus. 
[1492.]  Therefore,  for  a  more  extended  icnowletlge  of  the  art,  we 
must  study  the  earlier  history  of  architecture  among  the  Egyp- 
tians, Chaldeans.  Assyrians,  Persians,  Greeks,  Romans,  Frendi, 
(ierman  and  Englisli  nations. 

E(;yi'tiax.s.  Some  of  the  pyramids  were  erected  3500  to 
3000  B.  C.  ;  the  chambers  inside  were  accessil>le  by  means  of 
narrow  inelined  passages.  Stairs  do  not  appear  to  have  ever 
been  used  in  the  pyramids,  unless  perhaps,  in  some  opened 
recently  ;  but  in  the  tombs  of  the  same  date  tligiits  of  steps  are 
always  found,  i 

CiiAT.DKAXs.  Their  temples  were  sometimes  built  with 
oR-sets,  forming  a  terrace  every  story,  and  readied  by  flights  of 
steps  or  inclined  planes  from  one  story  to  the  next,  as  in  the  case 
of  the  Tower  of  Babel,  erected  29A7  B.  C,  which  is  described  in 
one  of  the  mosaics  at  St.  Marks,-  Venice,  showing  inclined 
boards  for  obtaining  access  to  scaffolding,  instead  of  ladders.  ^ 
Herodotus*  says,  "numbers  of  houses  were  three  and  four 
stories  high. 

AssYiUAXS.  Owing  to  the  scarcity  of  stone,  sun-dried  brick 
were  used  for  walls,  ami  probably  wood  for  rooling  and  interior 
tini.sh — hence  their  buildings  have  long  since  disappeared,  the 
ruins  scarcely  being  visible.  The  ruins  of  the  largest  royal 
palace  at  Nineveh,  erected  by  Sennacherib  about  704  B.  C, 
show  the  remains  of  an  inclined  plane,  ten  feet  wide;  close  by  is 
also  seen,  the  ruins  of  an  inclined  terraced  temple. 

Pkijsiaxs.  The  ruins  of  Persipolis,  the  ancient  capitol  of 
Persia,  show  the  palaces  to  be  reached  by  the  grandest  double- 
flight  of  platform  stairs  in  the  world.  =  The  stejjs  leading  to  the 
lirst  terrace  are  25'  7'^  wide;  the  rise  is  4^'  high  l)y  14'^  in  the 
tread  ;•'  there  are  flfty-five  rises  unconcealed  on  one  side  of  the 
platform,  and  forty-eight  to  the  landing ;  fiom  four  to  six  steps 
being  cut  from  a  single  block  of  marble.  A  second  double-flight 
leads  to  the  next  terrace  ;  steps  16'  long,  3"  rise  and  14"  tread, 
having  thirty-two  steps  to  each  flight;  ten  to  fourteen  steps  being 
cut  fnmi  a  single  block.  ^  The  sides  of  the  steps  are  walled  up 
and  decorated  with  sculptures,  representing  processions  bringing 
tribute  to  the  King.  These  palaces  formed  one  of  the  most  im- 
posing groups  of  buildings  ever  erected,  ami  is  said  to  have  been 
partially  burned  bv  Alexander  the  Great,  after  his  conqiu'st  of 
Persia  330  B.  C. 

1.  N.  ClilYord  liii'ker.  Professor  of  Aivliiteotuie.  iu  tlie  liliuois 
University. 

2.  ErectedOTC;— 1071  A.  r». 

'!.    Miirwick's  History  of  t^tair  Cases. 

4.  Flourished  484—408  B.  C. 

5.  Enrycloptedia  liritantiiea. 

t>.    Gwilt's  ])ictionai-y  of  Architecture. 
T.    Stuart's  Dictionary  of  Arehitecluie. 


10  IIjstoky  UK  Staik  Blilding. 

Jeki'SALem.  Solomon's  Temple  was  erecttcl  1011 — 1004 
B.  C.  Ezekiel  B.  C.  774,  iii  his  description  of  the  temple  locates 
nine  flights  of  steps.  This  temple  was  destroyed  by  the  Chal- 
deans under  Nebiichadnezzar,  B.  C.  588.  We  read  that  when 
the  Queen  of  Sheba  saw  "the  ascent  by  which  Solomon  went  up 
to  the  house  of  the  Lord,  there  was  no  more  spirit  in  her." 
Among  the  ruins  of  these  more  eastern  nations,  nothing  is  more 
remarkal)le  than  these  great  flights  of  steps.  The  builders  of 
tliose  days  among  the  Jews,  Chaldeans  and  Persians  so  far  as  we 
know,  were  the  only  people  who  really  understooil  the  value  of 
this  feature.  The  Egyptians  seem  wholly  to  have  neglected  it. 
and  the  Creeks  to  have  cared  little  about  it,  but  was  not  so  at 
Nineveh  and  Persipolis,  ^  for  from  the  indistinct  traces  left,  the 
stairs  must  have  been  one  of  the  most  important  parts  of  the 
design. 

Mexico.  The  Pyramids  of  Mexico  resemble  those  of  Assyria, 
being  terraced  and  having  inclined  planes.  The  Pyramid  of 
Papantlawas  seven  stories  high,  with  five  flights  of  steps  leading 
to  the  cell,  which  formerly  existed  on  the  top.^  This  prehistoric 
strncture  was  built  of  stone.  Baked  brick  was  mostly  used  in  the 
l)uilding  of  these  pyramids.     See  Prescotfs  Conquest  of  Mexico. 

Gkeece.  In  the  Ancient  Doric  Temple  of  Concoid,  at 
Agrigentum,  Island  of  Sicily,  [when  erected  unknown]  a  flight 
of  forty-one  steps^o  leads  to  the  roof  from  near  the  entrance; 
they  are  close,  being  constructed  in  the  thickness  of  the  wall. 
Similar  stairs  are  said  to  be  found  in  the  temple  of  Jupiter  at 
Olympia,  erected  about  435  B.  C. 

The  Syracuse  Theatre,  erected  480 — 406  B.  C,  had  eight 
radiating  flights  of  steps. 

The  Temple  of  Jupiter  at  Aizana,  has  a  grand  flight  of  out- 
side steps  98'  C  wide,  erected  about  140  B.  C. 

Komp:.  The  ancient  Romans  bori'owed  largely  from  the 
(Greeks  and  Etruscans ;  the  temples  and  theatres  of  the  Greeks 
served  as  models,  from  which  they  improved  aiul  built  up  their 
capitol.  Vitruviiis,  *  ^  however,  makes  no  mention  of  stairs  as 
being  an  impoilant  adjunct  of  the  dwelling  house;  if  the  stair 
case  had  lieen  of  much  consideration,  he  w(mld  have  most  likely 
described  them.  He  gives  the  numbers  3,  4  and  5  for  a  right 
angle  triangle,  and  suggests  the  hypothenuse  of  the  same  as  a 
good  proportion  for  the  inclination  of  a  flight  of  stairs,  liule, 
divide  the  whole  height  into  three  equal  parts,  and  take  five  of 
those  parts  for  the  length  of  the  inclination. 

The  stairs  in  the  Pantheon^''  are  triangular  on  plan,  so 
were  they  in  the  Baths  of  Caracalla.^^  jq  the  Baths  of 
Diocletian^ ^  the  stairs  were  built  between  walls,  in  the  same 
manner  as  we  build  l»ox  stairs  Ijetween  plastered  partitions.  It  is 
said  that  40,000  Christians  were  compelled  to  erect  this  stnicture 
to  appease  the  wrath  of  this  Roman  tyrant. 

The  summit  of  the  historic  column  of  Trajan^'  is  reached 
by  a  winding  staircase,  containing  185  steps ;  they  are  carved 
out  of  solid  blocks  of  marble  twelve  feet  in  length,  and  five 
feet  thick. 

s.  .lames  Ferguson's  History  of  Arcliitecture,  Vol.  1;  Pajre  192. 

9.  N.  Clilford  Kicker. 

10.  Josepli  Gwilt's  Encyclopaedia  of  Architecture. 

11.  Architect,  lie  nourished   under  Augustus  Ca?sar,  B.  C.  15;  he 
wrote  the  earliest  special  treatise  on  architectui-e  extant. 

12.  Erected  probably  20  B.  C. 

13.  Finished  about  217  A.  D, 

14.  Erected  about  302  A.  D. 

15.  Erected  114  A.  D. 


HlSTOKY    OF   bXAlli  BlILUINU.  11 

The  country  house  at  Pompeii  has  steps  with  a  rise  of  twelve 
inches.*®  The  Romans,  also  tlie  Greeks,  prided  in  wide  outside 
steps  at  tlie  main  entrance  of  tlieir  temples. 

Tlie  magnificent  temple  of  tlie  Sun  God  at  Baall;ec,  ^^  lias  a 
flight  of  outside  steps  164  feet  wide  between  the  buttresses. 

Of  the  thirty  odd  different  liinds  of  artisans,  advertised  for 
by  Constantine  the  Great,  for  the  building  of  Constantinople,  i" 
it  appears  "stair  hands "i^  were  required.  The  towers  and 
minarets  of  the  Mahometan  Mosques,  had  winding  inclined 
planes,  and  winding  stairs  to  reach  the  upper  stories  ;  sometimes 
the  stairs  were  built  winding  around  the  outside,  at  other  times 
they  were  built  in  the  thickness  of  the  walls. 

Italy.  In  this  beautiful  land  of  art,  during  the  middle 
ages  from  1000  to  1500  A.  D..  the  main  stair  cases  were  often 
constructed  on  the  outside  of  their  buildings,  the  climate  being 
more  favorable  than  in  the  more  northern  countries. 

In  court  yards  they  were  often  built  alongside  of  the  wall, 
and  supported  on  pillars  and  rampant  arches,  sometimes  they 
were  protected  with  a  raking  roof,  supported  by  columns,  set  on 
pedestals  at  regular  intervals,  and  balustraded  between  the 
pedestals:  these  outside  steps  were  often  treated  very  artistically 
for  dwellings,  public  buildings  and  palaces,  as  they  led  to  the 
principal  floor;  sometimes  they  were  double,  starting  from 
opposite  sides,  and  landing  on  a  spacious  platform  at  the  main 
enti'ance  to  the  building;  this  treatment  offered  a  good  chance 
for  architectural  display.  Marble  was  mostly  used  in  the  con- 
struction of  these  stairs.  Previous  to  1500  A.  D.,  very  little 
importance  was  attached  to  the  inside  stairs;  they  were  commonly 
built  in  the  thickness  of  the  walls. 

The  Campanile  or  Leaning  Tower,  at  Pisa,^"  is  circular  on 
plan;  the  external  diameter  is  53  feet,  and  the  height  is  183  feet; 
the  walls  are  13  feet  thick,  and  the  stairway  is  built  in  their  thick- 
ness, so  were  the  stairs  in  the  beautiful  Campanile,  ^^^  near  the 
Florence  Cathedral .  *  - 

The  open  newel  staircase  is  of  Italian  origin,  and  was  the 
invention  of  Nicola  of  Pisa, -^  1205 — 1278;  the  idea  was  after- 
wards utilized  and  improved  by  the  renaissance  architects  of  Italy, 
from  the  beginning  of  the  sixteenth  century. 

In  the  Belvedere  of  Pope  Julius  II,  1503 — 1518,  an  inclined 
plane  or  turn-pike  stair  case  of  five  revolutions  leads  to  the  upper 
story;  the  stairs,  or  inclined  plane  was  carried  on  continuous 
cylindric  vaulting,  and  is  supported  on  the  side  next  the  well 
by  eight  columns  in  each  tier.  ^*  The  architect,  Andrew  Palladio, 
1518 — 1580,  improved  the  art  of  stair-casing  during  his  day.^^ 

16.  ytuart's  Dictionary. 

17.  Erected  it  is  supposed  by  Antoninus  Pius  IAS— ICl  A.  D. 

18.  Founded  about  'dis  A.  D. 

19.  See  London  Building  News,  1S90. 

20.  Built  1174  A.  I). 

21.  Erected  at  tlie  beginning  of  the  Fourteenth  Century. 

23.  Tlie  Carupanile  iu  the  Piazza  of  St.  Marks,  Venice;  the 
heiglit  to  the  loggia  is  about  177  feet,  and  is  readied  by  a  ramp  or 
Inclined  plane,  making  thirty-si.x  rounds:  the  foundation  was  laid 
iu  888  A.  D. 

23.  A  noted  Architect  of  Pisa. 

24.  Marwick's  History  and  Construction  of  Stair-cases. 

2,).  He  says  'stair-cases  will  be  coniniendable  if  they  are  clear, 
ample  and  commodious  to  ascend;  inviting,  as  it  were,  people  to  go 
up.  They  will  be  clear  if  they  have  a  bright  and  equally  diffuse 
light;  they  will  be  sufficiently  ample  if  they  do  not  seem  scanty  and 
narrow  to  the  size  and  qualiiy  of  the  fabric.  But  they  should  never 
be  less  than  four  feet  in  widtli,  that  two  persons  may  pass  each  other. 
They  will  be  convenient  with  respect  to  the  whole  building  if  the 
arches  under  them  can  be  used  for  domestic  purposes;  and  with 
respect  to  persons,  if  their  ascent  is  not  too  steep  and  difficult,  to 
avoid  which,  the  steps  should  be  twice  as  broad  as  high." 


12  lIi.'iTOKy  OF  Stair  BTTii.Dixa. 

Many  circular  and  elliptical  stair-cases  were  constructed  through- 
out Italy,  of  a  stately  and  monumental  character.  The  Farnese 
Palace  stairs  is  73^  by  28^;  that  in  Carlo  Mademo's  Mattei  Talace, 
with  its  marble  walls  and  rich  stucco  ceilings,  65'  by  40';  that  in 
Ferdinando  Fugo's  Palace  Corsine  72'  by  45';  while  those  in  the 
workhouse  at  Genoa,  and  in  the  stupendous  unfinished  Royal 
Palace  at  Caserta,  Naples,  are  no  less  than  115'  by  63',  and  163' 
by  85' respectively.  Scamozzi,^^  1552 — 1616,  mentions  a  double 
winding  staircase  made  by  Pietro  del  Boyo  and  John  Cossiu  so  con- 
trived that  two  persons,  one  ascending  and  the  other  descending, 
should  never  meet.  This  style  of  a  stair- case  was  common 
tlirough  France  in  Mediaeval  times.  A  patent  was  taken  out 
in  our  own  country  for  tliis  kind  of  a  staircase,  by  W.  J.  Keim, 
New  York,  1868. 

The  well  of  the  staircase  in  the  Palace  Braschi.  by 
C.  Morelli,'-^  is  quadrangular,  40'  by  34',  having  straight  flights 
of  the  open  newel  style,  similar  to  those  of  to-day.  The  steps 
arc  ten  feet  long  each  in  one  piece,  supported  by  the  walls  at  one 
end,  and  resting  on  rampant  arches,  springing  from  columns  at 
the  outer  strings;  tlie  columns  are  sixteen  in  number,  and  of  red, 
oriental  granite;  they  stand  on  pedestals,  which  receive  a  broad 
railing  and  heavy  baluster,  which,  together  with  the  steps,  are 
of  white  marble. 

The  wall  side  is  decorated  with  pilasters  opposite  each  column 
and  a  half  balustrade  corresponding  to  the  outer  railing;  arches 
spring  from  the  columns  to  the  pilasters  across  the  soffit  of  the 
stairs,  forming  domical  vaulting  which  is  divided  into  panels,  and 
enriched  with  beautiful  frescoes.  The  spandrels  of  the  arches 
are  paneled  and  ornamented  with  carvings;  niches  are  formed  in 
the  walls  for  the  display  of  statuary.  This  design  of  Morelli's  is 
one  of  the  most  beautiful  staircases  in  Rome.  A  fine  illusti'ation 
of  two  stages  of  this  stair  case  may  be  seen  in  Marwick's  History 
of  Staircases. 

Fraxce.  During  the  first  century  A.  D.,  the  stairs  in 
France  were  constructed  similar  to  those  of  Italy,  Outside  steps 
were  sometimes  built  at  right  angles  to  the  building,  at  other 
times  parallel  to  the  same  resting  on  arches,  supported  by  piers; 
sometimes  they  were  roofed  over  to  protect  them  from  the  rain. 
During  the  first  centuries  the  tower  stairs  were  built  in  the  thick- 
ness of  the  walls. 

The  French  were  partial  to  the  winding  stairs,  they  are  to  l)e 
found  in  most  of  their  buildings  throughout  the  country,  from 
about  1000  to  1500  A.  D.  On  account  of  so  many  towers,  mostly 
square  or  circular  on  plan,  the  winding  staircase  suited  best,  and 
also  they  re(iuircd  less  room  in  their  construction.  They,  like  the 
Italians  first  built  the  well  for  the  staircase  square,  circular  or 
octagonal  on  the  plan;  later  on  for  their  public  buildings,  the 
ol)long  well  was  occupied  with  the  open  newel  staircase,  having 
straight  llights  and  quarter  pace  landings. 

After  1540  A.  D.,  the  French  Renaissance  style  became  more 
classical  and  dignified.  The  leading  French  architects  traveled 
extensively  in  Italy,  from  which  they  gathered  ideas  and  im- 
proved on  them  to  suit  their  taste  and  country.  The  churches, 
ehateaus  and  palaces  are  monuments  of  their  genius  and  skill 
as  architects  and  builders. 

2ti.    Stuart's  Dictionary  of  Architecture.    Scamozzi  is  said  to  be 
the  inventor  of  tlie  1  wo-foot  joint  rule,  also  the  angular  Ionic  Volute. 
27.    Flourished  1780  A.  D. 


HlSTOUY    OF   StAIK   BlILllINO.  13 

The  Chateau  at  Chateaudun,^^  jg  chiefly  noted  for  its  mag- 
nificent stone  winding  staircase,  one  of  the  finest  ever  con- 
structed.'^* Tlie  well  is  partly  square  and  partly  octagonal  on 
plan;  the  steps  wind  ai'ound  a  solid  newel  built  of  stone;  the 
steps  are  built  in  the  newel  and  walls  at  the  ends,  each  tread  is 
a  solid  stone,  rectangular  in  section  tliroughout,  giving  to  the 
soffit  the  same  appearance  as  above  ;  the  tread  and  rise  is  with- 
out nosing  and  scotia,^"  as  was  the  custom  in  Mediaeval  times. 
The  shaft  of  the  newel  is  deeply  cut  away,  to  form  a  bold  pro- 
jecting half  hand-rail  and  string,  which  winds  spirally  around  the 
newel ;  the  space  between  the  rail  and  projecting  base  or  string 
remains  plain  ;  at  the  junction  of  the  steps,  with  the  newel  on  the 
underside,  another  set  of  mouldings  project  from  the  newel, 
forming  a  cornice  ;  the  shaft  between  the  rail  and  cornice  is 
ornamental,  with  slender  columns  and  panels  between  the  columns; 
the  panels  are  elaborately  enriched  witli  carved  arabesques.  On 
the  wall  side,  engaged  columns  fill  each  angle,  extending  from 
the  steps  and  floors  to  a  projecting  cornice,  that  fills  the  angle 
made  by  the  steps  and  walls ;  at  the  upper  end  the  newel  is 
finished  with  a  cap,  from  which  spring  arched  semicircular 
groins,  to  connect  the  columns  in  the  angles  on  the  wall  sides, 
this  vaulting  gives  support  to  the  roof,  and  distributes  the  weight 
of  the  roof  and  vaulting,  partly  on  the  newel  and  partly  on  the 
walls,  and  gives  to  the  whole  a  beautiful  and  appropriate  finish. 

Many  beautiful  staircases  of  the  Renaissance  period  may  be 
found  throughout  France,  erected  after  the  beginning  of  the 
sixteenth  century. 

In  the  Chateau  Chambord,  ^^  *  a  double  staircase  is  erected, 
the  well  is  thirty  feet  in  diameter;  the  stairs  wind  around  a  hollow 
newel  ten  feet  in  diameier,  which  ends  at  the  terrace  level;  a 
smaller  stairs  is  built  in  this  hollow  newel  extending  beyond  the 
terrace,  where  it  is  terminated  by  an  elegant  circular  arctade 
crowned  by  a  circular  tower,  this  being  beautifully  decorated  with 
classical  columns  and  flying  buttresses.  These  double  staircases 
were  common  throughout  France,  they  were  luiilt  of  wood  and 
also  of  stone.  Owing  to  the  large  size  of  newel  required  in  this 
kind  of  stairs,  to  obtain  a  fair  width  of  tread  at  the  narrow  ends, 
a  third  winding  stairs  was  sometimes  constructed  inside  the 
newel;  at  otlu>r  times  the  space  is  divided  into  rooms,  and  at 
other  times  it  is  used  as  a  well.  Tlie  French  and  (iermans^?  often 
made  their  steps  and  rise  from  solid  oak  timber,  quartering  the 
log,  and  turning  the  heart  side  up;  this  made  a  solid  and  noiseless 
staircase.  Some  of  these  wooden  stairs,  built  during  the  middle 
ages,  are  still  to  be  seen  in  some  of  the  old  turrets  througliout 
that  country. 

Two  wooden  staircases  in  the  Holy  Chapel  in  Paris,  are 
probably  the  oldest  in  existence,  being  constructed  in  the 
thirteenth  century. ^s 

ExGLAND.  In  England  the  transition  began  in  the  reign  of 
Henry  VIII,  1509 — 1547,  from  the  Norman  conquest  1066,  up  to 
and  during  part  of  his  reign,  close,  or  blind  newel  stairs  walled 

28.  A  fine  illu.stration  of  two  stajres  of  this  staircase  may  be  seen 
in  the  American  Architect  and  Bulldin.t?  News;  of  September  17,  lK*;i. 
Erected  about  1408—1515  A.  D. 

29.  N.  Clifford  Ricker. 

30.  Parkei-'s  Glossary  of  Architecture. 

31.  Founded  1.526  A.  1). 

32.  The  Stadhaus  :it  Leyden,  Holland,  has  a  fine  outside  stairs 
built  at  the  beginnine  of  Uie  seventeenth  century.  See  illustration 
in  the  Aruerican  Architect,  for  March  27th,  1886. 

33.  Marwick's  History  of  Staircases. 


14  History  of  Stair  Building. 

up  ou  the  sides,  and  arched  over  in  the  form  of  a  tunnel  was  the 
prevailing  style;  at  the  angles  heavy  piers  projected  from  the 
walls,  finished  with  base,  and  cap  from  which  spring  groins; 
the  piers  were  low,  and  took  the  form  of  newels. 

In  the  reign  of  Queen  Elizabeth  1558 — 1603,  the  open  newel 
staircase  became  more  studied;  the  blind  straight  flights  between 
walls  were  modified  so  as  to  admit  light  above  the  hand-rail,  and 
in  place  of  balusters  the  space  was  close  and  sometimes  plastered 
under  the  rail.  This  gave  place  to  a  more  ornamental  construc- 
trou,  broad  short  flights,  with  elaborate  and  heavy  carved  newels 
at  the  angles, supporting  vases,  baskets  of  flowers,  minature  statues, 
columns,  lions  or  griffins.  In  this  reign  the  newels  formed  one 
of  the  chief  decorative  and  constructive  elements  of  the  design. 
The  hand-rails  were  broad  and  massive;  under  the  rail  was  filled 
in  with  fancy  cut  scroll  work,  or  heavy  tuined  balusters  set  ou  a 
close  string,  which  was  paneled  and  ornamented  with  bold  carved 
work,  and  finished  on  the  lower  edge  with  hanging  scroll,  termin- 
ating at  the  newels  in  the  form  of  pendants. 

This  and  the  succeeding  reigns  of  James  I,  I(j03— l'i;i5,  also 
Charles  1  reign  1625 — 1649,  the  balustrade  and  newel  occupied  at 
no  other  period  a  position  of  such  conspicuous  importance. 

The  decorative  feature  of  the  Elizabethan  staircase  arrived  in 
this  reign  at  its  zenith,  and  the  best  period  had  passed;  after  this 
tlie  style  had  bcome  more  debased. 

ytyle,  like  history,  repeats  itself;  at  the  present  and  near  the 
close  of  the  nineteenth  century,  we  are  copying  after  the  style  of 
Elizabeth  in  our  staircases,  with  short  flights,  close  outer  strings 
around  a  quadangular  well  hole,  with  massive  and  elaborate 
carved  newels,  sometimes  extending  to  the  ceiling,  and  finished 
with  arches;  at  other  times  the  newel  is  surmounted  with  statuary 
of  some  anti(iue  design. 

(Serious  objections  are  urged  against  this  style  of  staircasing — 
too  many  quirks  and  projecti(jns  for  catching  and  harboring  the 
dust,  and  the  expense  to  renovate  and  keep  them  in  a  good  sani- 
tary conditi(m;  indeed,  after  a  few  years  in  use,  it  is  impossible 
to  avoid  the  disease-breeding,  accumulations.  P'or  this  reason 
this  style  of  staircase  should  be  avoided  in  domestic  architecture. 
The  open  string,  and  return  nosings,  with  circular  turns  in  the 
angles  in  place  of  newels,  and  finished  with  turned  balusters  and 
a  continuous  hand-rail,  gives  a  more  cheerful  aspect  to  the  hall, 
with  less  expense  and  better  health  to  the  occupants. 

This  style  of  open  string  and  continuous  hand-rail  was  a 
great  improvement  over  the  old  ramn  and  knee  hand-rail  and  square 
well  hole.  In  England,  about  the  begiiming  of  the  eighteenth 
century,  the  .solid  newel  for  winding  stairs,  gave  place  to  the  open 
circular  well  hole,  with  rail  and  balusters,  thus  admitting  light 
and  air,  and  a  better  sanitary  condition  of  the  building. 

The  first  lines  i)ublislu'd  for  constructing  a  continuous  hand- 
rail, over  a  circular  well  hole  containing  winders,  was  by 
HaiJ'1'k>{kv,  of  London,  1725.  The  method  is  very  much  mys- 
.  tified^  *  but  shows  an  effort. 

The  ingenious  Mji.  Fuajscis  Fimci:,  was  tlie  next  in  1735. 
He  gives  a  method  to  draw  the  straight  ramp  and  knee,  also  a 
wreathed  ramp  and  knee  over  a  quarter  circle  on  plan;  also  a 
falling  mould  for  squaring  the  wreath  part;  also  a  method  to  find 
the  length  of  long  and  short  balusters  under  the  wreath  rail,  laid 
off  from  the  center  line  of  rail  on  the  stretchout.     He  also  gives  a 

34.  See  Peter  Nicholson's  Dictionary  of  Architecture,  by  Lomax. 
Page  76. 


HisTUKV  OF  Staik  Building.  15 

method  for  building  up  the  rail,  by  glueing  blocks  to  suit  the 
falling  line  of  the  rail;  he  also  gave  lines  for  the  construction  of 
the  scroll,  and  showed  how  to  ease  off  an  angle,  by  the  intersection 
of  lines;  he  made  use  of  ordinates  to  find  the  contour  of  raking 
mould  iugs. 

Ml!.  Laxglev,  17.38,  was  the  next.  He  shows  the  face- 
mould  for  the  quadrant  to  be  one-fourth  of  the  ellipsis,  having  the 
joints  of  face-mould  on  the  major  and  minor  axis  of  the  ellipsis, 
and  of  course  the  plank  would  be  canted  only  one  way,  without 
any  spring ;  this  would  require  very  thick  plank  to  form  the 
wreath  rail  over  winders,  spaced  equally  around  the  well  hole. 
He  made  use  of  ordinates  in  the  construction  of  the  face-mould. 

Mk.  William  Salmon,  1748,  was  the  next  author.  He  fol- 
lows Mr.  Price,  and  gives  the  lines  for  a  face-mould  over 
winders  around  a  circular  well  hole,  without  springing  the 
plank.  He  mentions  for  the  first  time  a  custom  among  workmen, 
the  method  of  glueing  up  the  rail  with  thin  strips  over  a  drum 
made  to  the  concave  diameter  of  rail,  when  enough  strips  were 
tlius  laminated  for  the  breadtli  of  the  rail,  and  the  glue  had  per- 
fectly dried,  the  twist  was  taken  from  the  drum  and  afterwards 
moulded  to  the  required  shape,  and  set  up  all  in  one  piece  over 
the  winders. ^'^ 

Mk.  AiiKAiiAM  SwAx.  1750  came  next,  and  was  fol- 
lowed by  Mr.  Willta:\i  Paixe,  1774.  In  the  "Practical 
Builder"  he  draws  the  face-mould  for  the  turnout  wreath-piece 
at  the  scroll,  in  the  same  way  as  shown  l)y  Mr.  Swan  ;  he  used 
ordinates  at  right  angles  to  the  hypothenuse  of  pitchboard.  At 
this  time  he  gave  two  methods  how  to  obtain  a  backing  for  a  hip 
rafter,  either  straight  or  curved.  Later  on,  he  issued  the 
"Builder,"  illustrating  various  kinds  of  stairs,  and  the  manner 
of  drawing  face-mould  for  the  same,  by  using  ordinates.  For 
winders,  in  a  semicircular  staircase,  having  straight  steps  above 
and  below,  he  shows  the  face-mould  drawn  so  as  to  make  the 
wreath  for  the  semicircle  all  in  one  piece ;  the  transverse 
axis  of  the  face  mould  being  plumb  over  the  chord  of 
semicircle;  the  face  edge  of  the  plank  would  coincide  with  the 
diameter  of  the  semicircle,  and  the  joints  connecting  the  straight 
part  would  be  spliced  joints,  for  the  plank  would  be  canted  only 
the  one  way;  hence  very  thick  stuff  would  be  re(iuired  to  avoid 
kinks  in  the  twist  part  of  the  rail.  Like  his  predecessors,  he  dis- 
covered the  wreath-piece  to  be  a  portion  of  a  cylindric  section, 
and  the  curve  of  face-mould  to  be  elliptical;  but  what  portion  of 
the  ellipsis  required  for  each  correct  face-mould  remained  a 
mystery. 

Mk.  Petek  Nicholson, 3«  in  1793  published  for  the  first 
time  his  "Carpenters  (luide,"  and  subsequent  editions  down  to 
1835.  He  cleared  away  some  of  the  mist  connected  with  the  con- 
struction of  the  face-mould;  he  discovered  how  to  draw  the 
elliptic  curve   through   three   points,    which  he   termed  resting 

;».  In  our  couiiiry  Mr.  Asheu  Bkn.jamin,  1792.  superintended 
the  erection  of  a  ciiculiir  staircase  in  the  State  House,  at  Hartford, 
Conuecticut.  Tlie  rail  was  Klued  up  of  strips  onc-eiglith  of  an  inch 
thick,  whifii  was  clainied  to  be  the  first  geometrical  rail,  over  a  cir- 
cular well  hole,  constructed  in  this  country. 

30.  Mh.  Petek  Nicholson  was  a  native  of  North  Britain;  he  was 
horn  on  tl)e  2ntV)  of  .Tuly,  1765,  in  the  Parish  of  Preston  Kirk,  in  the 
County  of  East  Lothian;  at  a  very  early  age  he  evinced  a  strong 
iiiechanical  genius,  and  also  a  turn  for  drawing  whatever  presented 
Itself  to  liim,  whether  of  animated  nature  or  otlicrwisc  ;  three  years 
instruction  was  the  most  he  ever  had  at  a  country  school,  which  he 
left  at  the  age  of  twelve.  Although  his  .scholastic  instructions  were 
very  limited,  he  was  bent  on  inquiry,  and  that  decidedly  of  a  mathe- 


16  HlSTOlty   OF   yxAiK   BriLDIXG. 

points;  one  point  at  each  end,  and  tlie  other  at,  or  near  the  center 
of  mould;  [not  certain  as  to  tlie  exact  location.]  This  new 
method  determined  that  portion  of  the  ellipsis  for  the  face-mould, 
over  a  (luarter  circle,  to  contain  the  minor  axis,  and  hence,  the 
mould  was  wider  at  each  end  than  at  some  intermediate  point, 
which  was  eijual  to  the  true  width  of  the  rail;  this  required  the 
plank  to  be  canted  two  wajs,  and  was  termed  the  •'springing"  of 
the  plank.  In  all  former  autliors  the  narrow  part  of  face-mould 
was  always  at  one  of  the  joints,  for  a  quarter  circle  on  plan, 
and  the  plank  was  canted  but  one  way. 

Not  being  certain  as  to  the  exact  location  of  the  center  resting 
point,  left  the  system  in  doubt  and  made  the  subject  an  abstruse 
and  difficult  task  for  the  learner,  and  also  for  the  more  jnactical 
man;  the  cutting  plane,  or  plane  of  plank  would  sometimes  be 
correct,  at  other  times  wide  of  the  mark. 

In  1849  Mk.  Jkakes  published  his  orthogonal  system  of 
hand-railing.  Mh.  Asiipitkl  published  a  work  on  hand-railing 
in  1S.51.  In  1853,  Mu  Josetii  (Jalimx  and  Mi:.  Lanoi.ey 
Banks  published  a  treatise  on  stair-casing,  in  which  the  systems 
practiced  by  several  stair  builders  of  London  were  published.  We 
will  notice  the  systems  of  Messrs.  Clark,  Foster,  Weston  and 
Perry. 

Mu.  William  Clauk's  method  to  find  the  face-mould,  was 
on  the  orthogonal  or  square  cut  principle;  he  makes  use  of  a 
parallel  mould,  cuts  the  joints  square  to  the  tangents,  and  finds 
the  joint  bevels  in  the  same  manner  as  Mr.  Kiddle  in  1855.  Mr. 
Clark  illustrates  his  principle  with  card  board. 

Mh.  Fostei;  also  shows  a  face-mould  on  the  orthogonal 
system,  the  mould  being  parallel  in  width. 

Mi:.  Weston's  metliod  in  some  particulars  is  similar  to  Mr. 
H.  Kiddell's  in  his  1855  and  1859  editions.  Jle  shows  the  devel- 
opment of  tangents  in  elevation  from  the  ground  plan;  he  finds 
the  angle  of  tangents  for  the  face-mould  correctly,  and  also  the 
joint  bevels  from  the  tangents  in  elevation;  he  makes  the  joints 
at  right  angles  to  the  tangents:  he  takes  a  point  from  the  diagonal 
on   plan,    for  the  center   of    all    face-moulds='^  at   the  angle  of 

matical  nfiiure.  At  the  ajje  of  twelve  he  assisted  his  father  in  his 
business,  but  did  not  relish  the  occupation  of  a  stone  mason,  and  at 
tlie  end  of  a  year  he  was  bound  to  scjve  for  four  years  as  an  appren- 
tice to  a  cubi'iu't  maker,  in  the  neijrliborinfr  villnse  of  Linton.  During 
his  Hppieiiticesliip,  younir  Nicliolson  enii)loyfd  every  leisure  mornenb 
in  iiiiproviii!i  liis  mind.  He  Ktudicd  alfiebra  assiduously,  from  day- 
lijllit  in  tlie  summer  morninjrs  till  six,  wlieii  lie  went  to  work,  as  well 
as  in  the  evenings  when  his  labors  were  over.  After  serving  to  the 
full  extent  of  liis  time,  he  went  to  Edinburgh  and  worked  at  his  trade, 
aud  studied  (he  higlier  branches  of  mathematics. 

At  tlie  age  of  t  wcnt.y,  he  came  to  London,  where  liis  uncle  named 
Hastil,  Ciiriicd  on  an  extensive  business  as  a  builder;  here  lie  still 
pursued  his  mathematical  studies  together  with  drawing;  .soon  his 
fame  spread  nmong  his  fellow  workman,  who,  anxious  to  improve 
themselves,  solicited  to  become  his  pupils;  he  opened  a  scliool  with 
aViout  ten,  the  fame  of  his  teaching  soon  brought  an  influx  of  pupll.'i. 
This  gave  Mr.  Nicliolson  more  leisure,  which  he  devoted  to  the  inven- 
tion and  anangement  of  an  original  treati.se  on  carpentry  and 
ioinery,  whicli  was  published  under  the  title  of  "Carpenters  New 
Guide,"  in  1702.  He  also  published  severiil  works  on  arcliitecture 
and  the  higher  liranches  of  mathematics.  He  commenced  his 
Architectural  Dictionary  in  1810,  and  finished  the  same  in  1819." 

Abstract  from  the  Memoirs  of  Peter  NiclwUon  by  John  Bown. 


S7.  Thi.s  point  taken  from  the  diagonal  on  ground  plan  and 
applying  the  same  to  the  diagonal  on  the  cutting  plane  for  the 
center  of  rail  is  correct  only  when  both  tangents  are  of  the  same 
length.  This  same  principle  was  published  some  time  ago  in  the 
"American  Builder,"^  by  IMr.  Langstaff. 


HlsTOKV   OF   SrAUi   BL1I.D1^0.  17 

taiigeuts  ou  the  cutting  plaue  through  which  he  finds  tlie  trace  of 
Ihe  center  line  of  his  face-mould,  by  using  a  pliable  strip,  froui 
liis  center  line  he  draws  the  concave  and  convex  curves  of  mould 
to  a  parallel  width. 

Mk.  W.  E.  rERKv's  method  differs  a  little  from  that  of  Mi'. 
Weston's:  he  finds  the  angle  of  tangents  for  the  face-mould  frtmi 
the  tangents  and  chord  in  elevation;  he  also  finds  the  directing 
ordinate  and  joint  bevels  from  the  tangents  in  elevation;  he  findr, 
the  center  line  of  rail  on  the  face-mould  correctly  by  the  use  of 
ordinates,  drawn  from  the  tangents  in  elevation  in  the  same  way 
as  Mr;.  Johx  Joxes  describes  in  his  1888  edition  of  hand-railing. 
Mr.  Perry  makes  use  of  a  parallel  face-mould.-*" 

Nkwi.and's  "Carpenters  and  Joiners  Assistant,"  18C0 — Mr. 
Nevvland's  treatment  of  the  cylindric  section  for  hand-railing,  is 
similar  to  that  of  Mr.  Nicholson. 

In  1864,  Mi:.  JosiirA  Jeavs  published  his  second  edition 
"The  Orthogonal  .Svstera  of  lland-railing,"  in  it  there  is  a  great 
deal  of  original  matter. 

In  1871.  Mk.  Geouge  Walton  published  his  "New Treatise 
and  Tractical  Guide  to  Stair-casing  and  Uand-railing,"  the  priuciplc 
is  the  same  as  published  by  Mr.  Kiddle,  in  the  1859  edition.  He 
shows  the  tangents  in  elevation  developed  from  plan:  he  finds 
the  angle  of  tangents  and  directing  ordinate,  also  the  joint  bevels 
from  the  tangents  in  elevation;  he  describes  the  trace  of  face- 
mould  with  the  trammel. 

In  1878,  Mi:.  William  Twiss  published  his  block  system  of 
hand-railing.  He  finds  the  parallelogram  on  the  cutting  plane 
direct  from  the  tangents  in  elevation,  and  recommends  tiie  traiu- 
mei  to  give  the  perfect  trace  of  face-mould:  the  joint  bevels  he 
finds  either  from  the  block,  cut  to  the  rake  of  the  tangents,  or 
from  the  tangents  in  elevation. 

Id  1882,  Mk.  Frank  O.  Cijesweli-  published  a  >mall  work 
on  hand-railing  and  stair-casing:  the  principle  is  similar  to  Mr. 
Riddle's  1859  edition  of  tlie  elements  of  hand-railing:  he  linds  the 
angle  of  tangents,  directing  ordinate,  and  joint  bevels  from  chord 
and  tangents  in  elevation,  developed  from  plan,  The  trace  of 
face-mould  he  finds  with  the  trammel. 

The  same  year,  188?,  Mk.  Geoi:ge  C'ollings  published  his 
•*  Practical  Treatise  on  Hand-railing.''  He  finds  the  parallel- 
ogram on  the  cutting  plane,  from  the  chord  in  elevation,  and  the 
hypothenuse  of  joint  bevels  from  the  parallelogram  on  the  cutting 
|)lane :  the  trace  of  lace-mould  he  draws  with  the  trammel:  the 
position  or  location  of  the  major  and  minor  axis,  he  determines 
i»y  the  trammel  and  rod  in  nearlv  the  same  way  as  shown  at 
Fig.  10  Plate  1. 

In  our  own  country,  Mk.  A.siiEK  Be^.jami.n,  in  18iil,  pub- 
lisiied  his  line?  for  the  construction  of  the  face-mould,  similar  to 
that  of  Mr.  NichoNon. 

In  18:38,  Mk.  Minakd  Lafevkk  issued  a  book  of  lines 
fur  the  stair  builder,  they  were  similar  to  Mr.  Nicholson's. 

In  18-10.  Mk.  -John  Hall  publislied  a  work  on  Hand-railing. 
He  claimed  an  improvement  in  the  formation  of  the  face-mould, 
l)y  the  use  of  the  Ellipsograph,  of  which  he  claimed  to  be  the 
inventor.     The  principle  is  to  draw  tlie  ground  plan  of  rail   on 


■'.■>.  Till'  four  i;is(  autlioj-s  show  llie  fufe-iiiould  diuwii  to  ;) 
l):ir:illol  widtli.  ciiiiul  lo  llie  Iruc  widUi  of  rail,  from  n  ceutt-r  liue; 
I  his  (iocs  not  <rive  a  correct  face-mould  foi'  llie  cyJiudric  section  on 
Ihe  ciittiiijr  plane.  Marl  Mr.  Perry  luadc  the  coiu-ave  and  convi^x 
>ides  of  his  facc-ir.ould  concentric  tlHnlic  ciuves,  his  system  would 
have  been  without  fault ;  his  ccutei- line  on  the  mould  is  tlie  correct 
cllii)tic  curve. 


18  History  of  Staiu  Buii.dixg. 

the  draught  board,  then  at  tlie  center  of  well  hole  erect  a  vertical 
shaft,  say  one  incii  in  diameter,  and  one  or  more  feet  long,  from 
which  extends  an  arm,  made  to  slide  and  turn  on  the  shaft,  the 
arm  to  Imve  a  pencil  fixed  near  the  end,  and  over  from  the  center 
of  shaft  equal  to  the  radius  for  the  concave  and  also  for  the  convex 
sides  of  rail.  Now  elevate  the  material  from  which  the  face- 
mould  is  to  be  made,  over  the  ground  plan  to  the  required 
inclination  of  wreath  piece  ;  then  move  the  arm,  and  the  pencil 
will  describe  the  elliptic  curve  of  face-mould  correctly  if  the 
material  has  the  correct  inclination,  lie  also  improved  Mr. 
Nicholson's  system. 

The  next  was  Mk.  Si.mox  De  Giiaff,  1S45.  lie  made  use 
of  the  ordinates,  but  claimed  tlie  invention  for  making  the  wieath 
for  the  semicircle  in  three  pieces.  This  work  of  Mr.  yimon  De 
Grafl',  was  the  last  book  published  exclusively  on  stair  buildiJig, 
on  the  Nicholson  system,  in  our  country. 

After  Mr.  Peter  Nicholson  issued  his  18.55  edition  of  the 
"Carpenter's  Guide,''  the  ingenious  Mi;.  Pi;tkk  Estkrhkook, 
stair  builder,  of  New  York,  was  led  to  investigate  the  subject  of 
hand-railing  more  scientifically,  as  to  the  uncertain  location  of  the 
center  resting  point  of  Mr.  Nicholson.  He  claims  to  have  made 
the  discovery  of  the  tangent  system,  thereby  locating  the  correct 
resting  point,  which  gives  the  true  inclination  to  tlie  tangents, 
from  which  the  cutting  plane  or  plane  of  plank  is  determined 
as  we  have  it  to-day;  Ln  1859,  in  company  witli  Mr.  J.  II. 
Monckton,  they  issued  a  work  on  stair  building. 

In  the  meantime  other  works  had  appeared  and  gave  to  the 
world  the  benefit  of  the  tangent  system.  In  1818,  Mk.  R.  A. 
Crrj'KH,  in  Ohio,  issued  his  fust  book  "The  New  Practical 
Stair  Guilder's  Guide,"  and  later,  1851,  his  "Universal  Stair 
Builder."  These  two  books  simiditied  the  theory  of  stair  build- 
ing, The  principle  being  correct,  it  gave  the  American  stair 
builder  a  much  easier  task  than  he  formerly  had. 

Mr.  Cupper  claimed  the  discovery  of  the  tangent  system,  and 
thereby  the  correct  resting  points;  also  to  be  the  inventor  of  the 
tangent  box,  of  which  he  gave  several  plates,  clearly  illustrating 
the  principle  of  the  tangent  system,  wliereby  the  stair  builder 
coiild  see  at  a  glance  the  whole  principle,  as  Mr.  Reynolds  says, 
in  a  "nut  shell."  lie  determined  \\m'  correct  position  of  the 
transverse  axis  and  the  priralletograui  for  tlie  face-mould  on  the 
cutting  pliine;  and  describes  the  niothod  of  cutting  the  crooks  out 
and  making  the  joints  .scpiare  to  the  face  of  plank;  the  use  of 
either  the  plumb  bevel  or  the  two  joint  bevels,  for  squaring  the 
wreath  piece;  the  drawing  of  tlie  face-mould;  either  with  a  string 
trannnel  or  by  ordinates;  in  fact  he  prepared  the  way  so  plain  for 
those  having  the  i)ractiee,  to  simplify  and  make  the  subject  still 
plainer  for  others  to  follow. 

In  1840  Mi:.  IIkyxoi/ds  issued  his  valuable  little  treatise 
and  supplement  for  the  stair  builders  library.. 

In  1850,  Mk.  David  (Jaav.  stair  builder,  of  Pittsburgh,  Pa., 
partially  prepared  a  work  on  the  subject,  i>ut  owing  to  a  fatal 
accident  the  work  was  never  completed.  He  lound  the  parallel- 
ogram or  angle  of  tangents  for  the  lace-mould,  direct  from  the 
chord  line  in  elevation,  and  described  the  face-mould  with  the 
trammel. 

In  1850,  the  ingenious  Mn.  Rir>i)i.K  issued  his  "Scientific 
Stair  Builder,"  in  which  he  determined  the  parallelogram  or  angle 
of  tangent  on  the  face-mould,  from  the  transverse  axis  on  the 
cutting  plane.  He  gave  a  greater  variety  of  stair  plans,  explained 
and  maile  plainer  the  government  of  the  tangents,  showed  how 


Ul.siXIUV    ol'    bTAIU   Litli-DXACi.  I'J 

tlio  joint  bevels  may  be  obtained  from  the  parallelof;iani  on  the 
cutting  plane,  and  the  general  application  ot  tlie  trammel  to  the 
construction  of  the  face-mould,  for  all  wreath  pieces  that  are 
circular  on  plan. 

In  1S55,  he  issued  his  secoud  edition  of  the  "Scientific  Stair 
Builder,"  in  which  he  described  the  parallelogram  or  angle  of 
tangents,  and  the  seat  of  trammel,  direct  from  the  inclination  of 
the  tangents  in  elevation.  He  also  described  tlie  underside  of 
rail  for  the  straight  part,  drawn  tlirough  the  center  of  baluster, 
for  Hie  correct  height  of  wreath  rail  in  tlie  cylinder. 

In  18.58  and  ISGO,  he  published  the  second  and  third  edition 
of  liis  "Elements  of  Hand-railing."  He  described  the  tangents, 
treads,  anil  rises  in  the  elevation  as  spread  out,  or  developed  from 
tangents  on  plan.  This  was  a  decided  improvement,  for  it  gave 
the  stair  builder  greater  control  over  the  inclination  of  tangents, 
and  allowed  the  length  of  the  odd  balusters  to  be  measured  from 
the  elevation.  Mr.  Kiddle  also  published  eight  or  ten  other  books 
for  the  benefit  of  the  stair  builder,  and  also  for  the  carpenter  and 
joiner.  He  died  March  lath,  1882,  at  his  home  in  Philadelphia, 
Pa  ,  loved  and  respected  by  all,  age  74  years. 

In  IS.-j.T,  Mr.  J.  K.  Pekkv.  of  New  York,  issued  a  work  on 
stair  building;  followed  in  the  same  year  by  Messrs.  Mii-wain 
and  Young.  They  found  tlu^  angle  of  tangents  direct  from  the 
chord  line,  and  used  a  parallel  mould. 

In  the  following  year,  1850,  Messrs.  Vaughn  and  Gi.enn 
published  a  small  work  on  the  subject.  They  used  the  parallel 
mould. 

In  1850,  Patrick  0"Neil,  of  Richmond,  Va.,  published  a  book 
for  the  stair  builder,  on  the  tangent  box  system,  much  the  same 
as  described  by  Mr.  Cupper,  in  his  first  book. 

Mkssus.  Eastei{15Kook  and  Moncktox,  in  1859,  issued 
•'The  American  Stair  Builder."  They  d(!scribed  two  ways  to 
find  the  angle  on  tangents  on  the  cutting  plane;  one  from  the 
transverse  axis  on  the  cutting  plane,  and  the  other  from  the 
tangents  in  elevation. ^a  in  the  former,  the  trammel  or  rod  is 
used  to  describe  the  curves  of  face-mould;  and  in  the  latter,  a 
pliable  strip  is  recommended  in  tracing  the  curves  of  mould. 

John  Thomas,  in  186a,  published  a  book  on  stair  building. 
The  principle  is  similar  to  that  published  by  Milwain  and  Young, 
and  also  by  Mr.  Langstaff.  The  angle  of  tangents  is  eased  off  by 
the  intersection  of  lines  for  the  trace  of  face-mould. 

In  1809,  A.  RussKTjj,  of  Memphis,  Tenn.,  published  a  very 
good  but  brief  work  on  hand-railing.  He  described  the  parallel- 
ogram or  angle  of  tangents  for  face-mould,  from  the  chord  line  in 
elevation,  and  used  the  tranunel  to  trace  the  curves  of  mould;  he 
found  the  joint  bevels  from  the  parallelogram  on  the  cutting 
plaric. 

In  1858,  Mi:.  C.  E  Loth  issued  a  very  good  book  on  stair 
building,  in  which  is  found  a  great  deal  of  interesting  matter  on 
the  subject.  He  finds  the  angle  of  tangents  from  the  transverse 
axis  on  the  cutting  i)lane,  and  the  trace  of  mould  through  points 
determined  by  ordinalcs. 

In  1S7'2,  also  in  1888,  Mu.  James  H.  Monckton  published 
two  works  on  the  subject;  in  the  former  he  described  the  angle  of 
tangents  from  the  diagonal  of  the  parallelogram  instead  of  the 
chord,    as   others   have   done.     He  also  described  the   curves  of 

;i9.  Tliis  iiietliod  of  fiiulitig  the  aii!;le  of  tangoiifs  was  piiTjlislied 
by  Mu.  K.  G.  IIatfiei.d,  \n  liis  "Ameiicuri  House  Carpenter,"  he  says 
it  was  invented  by  a  Mr.  Kells,  an  eminent  stair  builder  of  N.  Y.  City. 


20  History  of  Staik  Buii-DiNf^. 

face-mould  with  the  trammel.  In  the  latter  work  he  finds  the 
angle  of  tangents  from  the  chord,  and  the  trace  of  face-mould 
by  ordinates  drawn  from  the  tangents  and  a  flexible  strip. 

In  1873,  Mr.  William  Forbes  published  a  work  on  hand- 
railing,  called  the  "  Sectonian  Sj'stem."  This  method  is  similar 
to  the  tangent  box  system;  he  makes  use  of  a  parallel  mould. 

In  1874,  Mr.  J.  II.  Reaves,  of  Hamilton,  Canada,  issued  a 
work  on  stair  building.  He  finds  the  parallelogram  for  the  face- 
mould  direct  from  the  tangents  in  elevation,  and  the  curves  of 
mould  by  the  trammel,  similai  to  Mr.  Riddle  in  his  18.5.5  edition. 

In  1875,  Mr.  L.  D.  Gould  added  his  book  to  the  stair 
Imilder's  list.  In  it  there  are  some  original  ideas.  He  finds  the 
axis  on  the  cutting  plane  from  the  chord  and  diagonal  on  plan, 
and  the  angle  of  tangents  from  the  axis  on  the  cutting  plane.  He 
makes  use  of  the  string,  to  trace  the  curves  of  face  mould,  similar 
to  Mr.  Riddle,  in  some  of  his  later  works. 

In  1880,  Mr.  R.  J.  Sherratt  published  his  book  on  hand- 
railing.  He  finds  the  angle  of  tangents  from  the  transverse  axis 
on  the  cutting  plane,  and  the  trace  of  mould  with  a  string. 

In  1S84,  Mr.  F.  T.  Hodgson  published  a  treatise  on  stair 
building,  the  title  of  which  is  "Stair  Building  Made  Easy.'- 
Another  publication  by  an  "Old  Stair  Buildei?,"  appeared  in 
1885,  entitled  "A  New  System  of  Hand-railing."  The  system  is 
similar  to  Mr.  Weston  and  W.  E.  Perry's,  and  later  Mr.  Jones. 

In  188',»,  Mr.  J.V.  Secor  issued  a  work  on  Hand-railing.  He 
finds  the  parallelogram  for  the  face-mould  direct  from  the  chord  in 
elevation,  and  the  bevels  from  the  parallelogram  on  the  cutting 
plane.  All  the  above  works  are  not  w-ithout  some  merit  to  the 
diligent  imiuirer  after  a  thorough  knowledge  in  the  art  of  stair 
building. 


PLATE  I. 

Geometry. 

Figure  1.  A  point  has  position  but  not  magnitude,  as  at 
A,  Since  a  true  point  has  no  size,  a  line  has  no  breadth.  A  line 
is  the  patli  of  a  point  in  motion,  but  as  we  make  lines  they  of 
conrse  have  breadth.  Lines  are  termed  right,  or  straight  lines, 
curved,  or  mixed. 

Fig.  2.  JBC  shows  a  strakjht  line,  having  length  and 
l)readth,  but  no  thickness;  is  composed  of  points,  and  if  straight 
is  the  shortest  distance  between  any  two  given  points. 

Fig.  3.  Shows  parallel  ZfJies,  which  may  be  straight  as 
DE  and  FG,  or  curved  as  HXI  and  JXK,  Fig.  5  ;  and  if  pro- 
longed they  would  be  eriually  distant  from  eacli  other  throughout 
their  extension. 

Fig.  4.  A  (turvcd  line  LMN,  is  one  that  does  not  lie  in  a 
straight  line  between  its  extremities,  it  may  be  regular  or  irregu- 
lar as  OPR,  Fig.  8. 

Fig.  5.  Parallel  curved  lines,  HXI  and  JXK,  are  such, 
provided  they  are  everywhere  the  same  distance  apart;  if  they 
are  circles  they  will  be  concentric. 

Fig.  6.  Hhoyvs  n.  mired  or  compcnind  Ime,  STVW,  being 
part  straight  and  part  curved. 

Fig.  7.  A  zufrmg  line,  AB,  is  composed  of  a  series  of 
straight  lines  as  tiie  Chevron  Moulding  in  the  Norman  Archi- 
tecture. 

Fig.  8.  An  irrcgnlar  or  mixed  curve,  as  OPR,  is  used  in 
landscape  gardening. 

Fig.  9.  <^onverginci  lines,  CD  and  EF,  if  prolonged  will 
converge  at  0/  they  are  also  called  oblique  lines. 

Fig.  1.0.  Horizontal  line,  AB,  indicates  a  level  or  hori- 
zontal line,  and  is  at  right  angles  to  a  plumb  line.  The  surface 
of  water  at  rest  is  always  horizontal.  Perpe^idlc.ulnr  line,  CD, 
is  i)erpendicular  to  AB  ;  any  line  may  be  said  to  be  perpendicular 
to  a  right  line.'  when  the  angle  is  a  rigid  angle,  or  an  angle  of 
110  degrees  as  BCD.' 

Fig.  11.  Acute  angle  :  an  angle  that  is  less  than  a  riglit 
angle,  as  ABC. 

Fig.  12.  Obtuse  angle  :  an  angle  that  is  greater  than  a 
right  angle,  as  ABC. 

Fig.  13.  CurviUnear  angle.  The  angle  OHJ,  formed  by 
the  intersection  of  curved  lines.  And  when  the  angle  is  formed 
by  straight  and  curved  lines  they  are  termed  mixtilinear  angles, 
as  KLM. 

t.    A  iMj;hf,  line,  is  a  .sffuishl  liiu'. 

i.    In  cU'scril)ing  ;ui  angle,  t  lie  iniddk'  loller  detiutes  the  itiiiiif , 


23  Plate  1. 

Fig.  14.  Diagonal  line ;  is  a  line  joining  two  opposite 
angles,  iiom  corner  to  corner,  as  AB. 

Superficies. 

A  surface  has  lous^tli  and  breadth,  but  no  thii-kness,  foi-  instance: 
a  shadow  gives  a  good  representation,  its  length  and  bre;idtl»  can  be 
measured,  but  not  its  depth.  A  .solid  has  length,  breadtli  und  thick- 
ness. 

A  Playie  Figure,  is  a  portion  of  a  plane  enclo.sed  on  all  sides 
with  lines;  when  the  lines  are  straight,  the  figure  is  termed  a  ipolynan 
or  rectilineal  fiqure.  Polygons  have  different  names,  according  to 
the  number  of  their  sides,  and  means  a  many  angled  or  sided  figure. 

A  Polygon  of  three  sides,  is  iitrimigle;  of  four,  a  quadrilateral;^ 
of  five,  a  peutagon;  of  six,  a  hexanon;  of  seven,  a  heptufjon;  of  eight, 
an  octaaon;  of  nine,  a  nDiiagon;  of  ten,  a  deeagon;  of  twelve,  a 
dvdecagon. 

A  Reijidar  Polygon,  is  a  polygon  whose  sides  and  angles  are  equal, 
each  to  each,  and  its  perimeter  Is  the  sum  of  the  bounding  lines. 

A  Parallelogram,  is  a  quadrilateral  which  has  its  opposite  sides 
parallel.  There  are  four  kinds,  the  square,  rectangle,  rhombus  and 
rhomboid. 

Fig.  15.  A  sq\iare  has  its  four  sides  equal,  and  all  the 
angles  are  right  angles,  as  at  A,  JB,  C,  D.  The  enclosed  angles 
at  E,  F,  G,  H,  are  termed  intertuU  (imjles;  at  A,  B,  C  and  D, 
they  are  termed  external  angles. 

EoLE  — To  find  the  area,  square  one  of  the  sides.  Example:  16 
0"X16'  0"=256  feet.    Ans. 

Fig.  16.  A  rectangle,  is  a  parallelogram  whose  angles  are 
right  angles,  and  the  opposite  sides  only  are  of  equal  length,  as 
ABCD. 

RuLK.— To  find  the  superficial  area,  multiply  the  length,  23'  0"  by 
the  breadth,  IG'  0".    Example:  2:i' 0"X10' 0"=y58  feet.    Ans. 

Fig.  17.  A  rhombus  ABCD,  is  a  parallelogram,  having 
all  lour  sides  (Kinal  in  length,  but  only  the  opposite  angles 
equal.     This  ligiire  is  sometimes  termed  lonenge, 

Rule.— To  find  the  area,  multiply  the  side,  IC  0"  l)y  the  altitude* 
EA,  14'  0".    Example:  16'  0",<14'  0"=224  feet.    Ans. 

Fig.  18.  A  rhotnhoid,  is  a  parallelogram  liaving  both 
opposite  sides  and  opposite  angles  equal  ;  or  two  of  whose  sides 
are  greater  than  the  other  two. 

Rule.— To  find  the  area,  multiply  the  length,  IS'  0"  by  the  altitude 
^E.  16'6".    i!/'.«-amjjie;  18'0"Al6'6"-2i)7feet.    Ans. 

A  triangle,  is  a  polygon  bounded  by  three  straight  lines,  contain- 
ing three  angles.  There  are  four  kinds,  the  rigid  a)tgle  triangle,  the 
equilateral,  the  scalene,  and  the  iso.'<celi's  triangle. 

Fig.  19.  A  right  angle  triangle,  ABC,  has  one  right  angle 
and  two  acute  angles  ;  the  .side  AB,  opposite  the  right  angle  is 
termed  the  hypolhenuse,  the  side  AC,  the  base,  and  the  other 
side  CB,  the  perpendicular.  Fig.  19  is  known  among  builders 
as  the  (i,  8  and  10  triangle,  for  scpiariiig  the  foundation  walls  of 
buildings. 

Rule.— To  find  the  ai'ca,  multiply  the  length  of  the  base,  6'0"  by 
one-half  the  perpendicular,  S' 0"-h2=4  feet.  Example:  (5' 0">  4' 0"^ 
24  feet.  Ans.  This  rule  answers  for  all  triangles,  for  a  triangle  is 
one-half  a  laarallelogram,  having  the  same  base  and  altitude. 

3.  Quadrilateral,  is  a  plane  surface  inclosed  by  four  right  lines. 
There  are  three  classes  of  quadrilaterals;  namely,  trapezoida,  trape- 
ziums and  Parallelograms. 

4.  The  altitude  of  a  parallelogram  is  the  distance  between  its 
opposite  sides;  of  a  trapezoid,  it  is  the  distan(;e  l)etwoeu  its  parallel 
sides;  of  a  triangle,  it  Is  the  distance  from  any  vertix  to  the  side 
opposite,  or  to  tliat  side  prolonged  as  CD,  Fig.  22. 


Plate  2.  23 

Rule.— To  find  the  length  of  hypothenuse  AB,  when  the  base  AG 
and  the  perpendicular  BC,  are  given.  Add  together  the  squares  of 
the  base,  and  perpendicular,  and  the  square  root  of  the  sum  will  be 
the  length  of  the  hypotlienuse.    Example:  6?  +82 -v"' 100=10  feet.   Am 

This  rule  is  valuable  to  carpenters  and  builders,  when 
estimating;  for  finding  the  length  of  valleys  and  hips,  also  the 
length  of  braces,  and  figuring  for  the  strains  in  the  same.  Every 
young  man  should  study  well  this  problem. 

To  find  the  length  of  base  or  perpendicular,  when  the  hypoth- 
enuse, and  either  one  of  the  other  sides  are  given. 

EULE.— From  the  square  of  the  hypothenuse,  subtract  the  square 
of  the  side  that  is  known,  and  the  square  root  of  the  remaiiider  will 
be  the  length  of  the  unknown  side.  Example:  lO?'— 82'=v''36'=G  feet. 
Ans. 

Fig.  20.  An  equilateral  triangle.  The,  three  sides,  AB, 
BC  and  CA,  aud  the  three  angles  at  A,  B  and  C,  are  equal, 
and  are  equal  in  area  to  one-sixth  of  a  hexagon  whose  sides  are 
the  same,  and  the  given  side  BC,  is  equal  to  the  radius  of  a 
circumscribed  circle.  The  cooper  to  find  the  radius  of  a  barrel 
head,  sets  the  dividers  so  as  to  step  around  in  the  groove  just 
six  times. 

Rule.— To  find  the  area  multiply  the  length  of  the  base  BC,  16'  0" 
l)y  half  its  altitude  EA,  13.40  feet.  Thus,  10'  0"Xi?'.»r-107.n2  feet. 
superH(;ial.    Ans. 

Fig.  21.  An  Isosceles  Triangle.  ABC  has  two  sides  equal, 
and  all  the  angles  are  acute. 

Rule.- To  find  the  ai-ea,  multiply  the  base.  BC,  [1.5'  0"]  by  half  the 
altitude,  EA,  I?/)'  0"]  thus;    15'  0"X20^0"=1.V  0'  feet.    Am. 

2 

Fig.  22.  A  Scalene  Trianr/le.  ABC  has  one  obtuse  and 
two  acute  angles,  the  angle  BCA  being  obtuse,  its  altitude,  AD, 
is  found  by  prolojiging  the  base  line  BC  to  D.  The  area  is  found 
in  the  same  manner  as  at  the  preceding— by  multiplying  Ihe  base 
by  half  its  altitude. 

Fig.  23.  A  Trapezoid,  ABCD,  is  a  quadrilateral  which 
has  two  of  its  sides  parallel  to  each  other,  as  AB  and  CD. 

Kui.E— Tofind  the  area,  multiply  the  sum  of  the  parallel  sides, 
AB,  [20' 0")  and  CD,  [•.'(/ 0"]  by  the  altitude.  Kn,  [10'  0"1,  and  half  the 
product  will  lie  tlie  aiea.  Example:  2(;' 0";  20' 0"=l(J'\tl'O"=G 4  4=322 
feet.    Am.  * 

Fig.  24.  A  Trapezium.  ABCD  is  a  quadrilateral  which 
has  no  two  of  its  sides  parallel  to  each  other. 

Rule. — To  find  the  ajfii,  multiply  the  diagonal,  CB,  [2(5' 0"]  by  tlie 
sum  of  tlie  two  pcrixMiiHrnl,!  is,  AE,  [IS' 0"]  ;ind  DH,  [(i'O"],  falling 
upon  it  from  the  opposli/'  mi'zh-s,  and  half  the  product  will  be  the 
area.    Example:  is' 0"  i  D' 0"..2(i' a"=5?i  ^312  feet.    Am. 


PLATE   2. 

The  Cikcle. 


Fig.  1.  A  circle,  ABCD,  is  a  plane  figure  bounded  by  one 
line  which  is  termed  the  circumference,  and  is  equal  to  360 
degrees,  and  it  is  such  that  all  straight  lines  from  a  certain  point 
within  the  figure  called  the  center,  to  the  circuint'ereuce,  are  equal 
to  one  another,  and  the  space  within  the  whole  circumference  is 
termed  the  circle. 


24  Plate  2. 

Tlie  diameter  of  a  circle  is  a  straight  line  drawn  through  the 
center  at  O,  and  terminated  by  the  circumference  at  AC,  dividing 
tlie  circle  into  two  semi-circles.  The  rddius  of  a  circle  eiiuals 
lialf  the  diameter  ;  the  span  of  the  dividers,  when  describing  the 
l>ouudary  of  any  circle  is  termed  the  radius,  as  OC.  When  more 
than  one  line  radiates  from  the  center  to  the  circumference  they 
are  term';d  the  radii,  as  OM,  and  ON. 

IJl'JjE.— To  find  the  area  of  a  ch'cle.  Siiuare  the  rtiainetor  AC, 
(2(/ 0"),  and  niuUiply  by  the  decimal  .7854.  fi-rami^te:  20' 0"X20'0"X.7S.>t 
=;}4(i..36  square  feet.    Ans. 

The  diaiueter  being  given,  how  to  find  Ihe  circutnferoucc. 

KUI.E.— Multiply  the  diameter  by  the  constant,  3.1416.  E.nttitiilc: 
•:<)'  0">ca.l4IO-62.8:j20  feet.    Ans. 

A  taviient,  to  a  circle,  is  a  straight  line,  which  touches  tlie 
circumference  but  does  not  intersect  it  liow  far  soever  tiie  line  be 
produced,  as  EF.     An  arc  is  part  of  a  circumference. 

Fig.  2.  A  semicircle,  ABC,  is  tlie  figure  contained  by  a 
diameter  and  that  part  of  tlie  circumference  cut  off  by  tlie  diame- 
ter AC,  and  is  equal  to  180  degrees. 

Pig.  3.  A  quadrant  of  a  circle,  is  the  half  of  a  semicircle 
bounded  by  the  arc  ABC,  and  the  two  radii,  OA  and  OC,  and  is 
equal  to  'JO  degrees. 

Fig.  4.  A  chord  i>  a  straight  line  joining  any  two  points  in 
a  circumference,  but  not  passing  through  the  center,  as  C  E.  A 
segment  is  that  ))ortiou  of  the  circle  contained  between  the  cliord 
AB  and  the  arc  ACB.  CD  is  the  Versed  sine.  How  to  find  the 
diameter  of  a  circle  when  the  chord  and  the  versed  sine  are  given. 
Let  the  chord  AJ5  equal  ;JO'0"aud  the  versed  sine  CD  equal  6'  0". 

KuM-;  —Divide  the  square  of  half  the  chord  by  the  versed  sine;  to 
1hi.s  product  add  tlie  length  of  the  versed  .sine,  and  the  result  will  be 
I  lie  length  of  tlie  diameter  of  the  circle,  of  wliicli  the  arc  of  the  circle 
is  a  pari,  i'/'.rrtmjjfc  ;  3  6^18x18  3|4=-54  (5 -60  ft .  Aii^.  The  radius 
v.ill  cqmil  llie  half  of  (»'  or  :jO  feet. 

Fig.  5  shows  two  concentric  circles,  AB  being  the  outer 
diameter,  20'  0'^  and  CD  the  inner  diameter,  IG'  0'^. 

Rule— To  find  the  area  of  the  space  included  between  the  circuiii- 
fevence  of  the  concentric  circles.  Multiply  the  sum  of  the  two  diame- 
ters by  their  difference,  and  this  product  again  hy  the  decimal  .7854. 
t'j. rat n'plr:    10  r20    :J6x:4/..7854  -l]:i.o;i,  area  rcciuired. 

Fig.  6.  ABCD  shows  the  convex,  or  outside;  and  EFGH 
shows  the  concave,  or  inside  of  a  curved  surface. 

IVnOHLFMS. 

Fig.  1.  Ti)  bisect  a  (jUien  Vine.  L't  AB  be  the  given 
straight  line,  from  the  points  A  and  B  as  centers,  with  any  div 
lance  greater  than  half  AB.  describe  arcs  cutting  each  other  at 
C  and  D.  Draw  the  line  CD,  and  the  jioint  E,  wliere  it  cuts 
AB,  will  be  the  middle  of  the  litie  recpiired.  CD  will  also  be 
perpendicular  to  the  given  straight  line  AB;  and  the  angles  will 
all  be  right  angles. 

Fig.  2.  From  a  'jivcn  (mint  ouUiidc  of  a  'jioen  straiyhl 
line,  to  let  fall  a  j>erT>endicvlar  to  the  fjivcn  straight  line.  Let 
A  be  the  given  point,  and  SC'the  given  straight  line.  WitJi  any 
radius  greater  than  AH,  describe  arcs  from  the  center  A,  cutting 
^Cal  D  and  E.  Again,  with  any  radius  greater  than  half  DE, 
draw  arcs  from  D  and  E,  intersecting  at  F.  Join  FA,  cutting 
DE^tH;  then  i?A  will  be  perpendicular  to  BC,  and  ))assing 
Ihrough  the  given  point  A,  as  required. 


Plate  2.  25 

Fig.  3.  To  set  up  a  perpendicnlar  at  the  end  of  a  given 
lijic.  A^.  From  A  and  B  describe  arcs  of  equal  radius  inter- 
secting in  D,  then  with  the  same  radius  draw  tlie  semicircle  from 
S  throufih  A  to  C ;  draw  BD  produced  to  intersect  the  semi- 
circle at  C,     Join  CA,  then  CA  is  the  perpendicular  required. 

Fig.  4.  Another  method..  I-et  AB  be  the  given  line,  and 
A  the  point  to  erect  the  perpendicular.  Witli  equal  radii  from  A 
and  B,  draw  arcs  cutting  at  C ;  through  BC  draw  the  straight 
line  produced  to  D,  make  CD  equal  BC.  Join  DA,  then  DA  ia 
the  perpendicular  required. 

Fig.  5.  Another  metliod  to  erect  a  perpendicular  near  the 
end  of  a  given  straight  line.  I^et  AB  be  the  given  straight  line, 
take  any  point  as  C,  and  any  radius  greater  than  AC,  and  des- 
cribe arcs  at  D  and  E;  then  take  another  point  J*,  and  descrilx' 
arcs  intersecting  at  D  and  E.  Join  D  and  E,  then  the  line  DE 
will  be  the  perpendicular  required. 

Fig.  6.  To  erect  a  perpendicular  from  a  given  point  D, 
on  a  given  curved  line  ABC.  From  the  point  D,  describe  ares 
with  equal  radius,  cutting  the  given  curved  line  at  .Band^; 
again,  with  equal  radius  describe  arcs  from  the  points  JBand  F, 
intersecting  at  jRT.  Join  KD,  then  the  line  KD  will  bo  perpen- 
dicular or  normal  to  the  given  curved  line  ABC. 

Fig.  7.  To  erect  a  perpendicular  to  a  given  curved  line 
ABC,  from  a  point  J,  outside  the  given  line.  With  any 
radius  greater  than  the  distance  from  J^ to  the  given  line,  draw 
the  arc  cutting  the  curved  line  in  K  and  L;  also  draw  arcs  with 
equal  radius  from  Kand  L,  intersecting  at  M.  Join  MJ,  cutting; 
the  curved  line  in  JP,  then  JP  will  be  tiie  perpendicular  required. 

Fig.  8.  Three  points  ABC,  out  of  a  straight  line  being 
'jiven,  to  find  the  center  of  a  circle  so  that  the  three  points  mrnj 
he  in  the  circumference  of  the  circle.  From  C  and  B,  witii 
equal  radius,  draw  arcs,  cutting  at  2  and  3.  Also  from  A 
and  B.  with  equal  radius,  draw  arcs,  cutting  at  4  and  .5.  Join 
4  and  .5  iiroduccd,  also  join  2  and  o  produced,  intersectin:r  at 
D;  then  D  is  the  center  to  sweep  through  the  three  points  ABC, 
as  required. 

Fig.  9.  Tlic  span  AB,  and  height  CD,  of  a  segment 
hring  given,  to  find,  the  cealrr  E,  to  drdin  the  cu)~ve  ADB. 
With  any  radius  greater  tlian  half  AB,  draw  arcs  from  the  points 
A  and  B,  intersecting  each  other  in  2  and  3.  Again,  with  any 
radius  draw  arcs  from  the  ))oints  A  and  D,  intersecting  each  other 
in  .5  and  4;  Join  5  and  4  produced,  join  3  and  3  jiroduced,  inter- 
secting at  E;  tlieu  E  is  the  center  to  sv/eep  the  arc  through 
ADB. 

Fig.  10.  Aniilhcr  method.  The  span  AB,  and  height 
CD,  being  given.  With  any  radius  greater  than  AC,  and  Avith 
A  and  B  for  centers,  draw  arcs  intersecting  at  E;  join  ED, 
draw  the  chord  nt  AD.  With  the  ))oints  A  ancl  B  for  centers, 
draw  the  arc  2-3,  also  4-5  indelinite.  Make  4-.5  equal  2-3; 
join  A~),  prolonged  to  intersect  DE  at  H,  for  the  center 
required. 

Fig.  11.     Anollicr  melliod.     The  chord  or  sp%n  AB,  and 
height  CD,  being  given,  to  siveep  the  arc  ADB,  uhthoul  finding 
It  center.     In  very  llat  arches,  and  wide  span,  or  when  the  radius 
is  very  long,  this  method  may  serve  a  good  purpose, 
3 


26  Pr.ATE   3. 

At  A  and  B  tack  a  lOd  wire  nail,  then  talie  two  strips  five 
inches  wide,  and  a  few  inches  longer  than  the  span,  let  them  be 
jointed  straight  on  one  edge;  now  place  one  strip  to  line  AD,  and 
the  other  strip  to  line  DB,  have  the  jointed  edge  against  the 
nails,  cross  and  nail  them  together  at  D;  see  that  the  strips  are 
close  to  the  two  nails,  then  near  the  end  tack  on  a  brace.  Now 
hold  a  pencil  in  the  angle  at  D,  and  move  the  triangle  against  the 
nails,  and  toe  pencil  will  describe  the  curve  required. 

Fig,  12.  A  circle  ABC,  and  a  inngent  DE,  to  tha  circle 
beincj  given,  to  find  the  point  of  contact.  Take  any  point  in  the 
tangent  DE,  as  2;  draw  2F  bisect  3  JP  at  H,  and  with  tlie 
radius  If^,  describe  the  semicircle  2KF,  cutting  the  tangent  and 
circle  in  K,  then  K  is  the  point  of  contact  required. 

Fig.  13.  The  arc  of  a  circle  ABC,  and  the  iangr.nt  LD, 
heiuff  given,  to  find  ilie  jmhit  of  contact,  the  center  of  the  circle 
being  unknown.  From  any  point  as  D  on  the  tangent,  draw  any 
line  cutting  the  arc  as  DFE;  bisect  DE  in  O,  then  with  OE  for 
a  radius,  draw  the  semicircle  EHD.  At  i^  erect  a  perpendicu- 
lar to  ED,  cutting  the  semicircle  in  K,  then  with  D  as  a  center, 
and  DKior  a  radius  draw  the  arc  KL,  cutting  the  given  arc  in 
L  for  the  point  of  contact  as  required. 

Fig.  14.  To  drav)  a  tangent  to  a  given  circle  ABC,  t'"it 
,f hall, pass  throvgli.  a  given  point  A.  From  the  center  O,  draw  OA 
through  the  point  A,  draw  EF  perpendicular  to  OA;  then  EF 
is  the  tangent  required. 

Fig.  15.  A  triangle  ABC,  hchig  given  to  dravi  a  circle, 
tluit  ivM  be  tangott  to  three  given  side-;.  Bisect"  the  angles  at 
A,  B,  C,  and  the  intersection  at  O  wiil  give  the  center  of  the 
circle  required. 


PLATE   3. 

I'KOKLEMS. 


Fig.  1.  To  bisect  a  given  angle  ABC.  WiMi  any  radius, 
and  JB  as  a  center,  describe  arc  culling  AB  and  BC  in  D  and  E; 
again,  with  X)  and  J57  as  centers,  describ(;  arcs  intersect insr  in  F; 
join  BF,  then  the  angle  FBA,  is  equal  to  the  angle  FBC. 

Figs.  2  and  3.  To  transfer  an  angle  B,  A,  C,  Fig,  .". 
e<pial  to  a  given  angle  3,  2,  4,  Fig.  2.  With  any  radius,  and  2 
as  »  center,  draw  the  arc  3,  4  ;  then  with  the  same  radius,  and  A 
as  a  center,  draw  the  arc  BC;  make  ^C equal  o,  4  ;  join  AC, 
then  the  angle  CAB  will  equal  the  angle  3,  2,  4,  required. 

Fig.  4.  From  a.  gieen  straight  line  AB  to  eonstmrt  a 
square.  With  A  and  B  as  centers,  and  AB  for  a  radius,  describe 
arcs  intersecting  at  C  and  prolonged;  again,  with  A  and  C  as 
centers,  and  etiual  radius,  draw  arcs  intersecting  at  E;  join  EB, 
cutting  the  arc  ADC  m  D;  then  with  CD  for  a  radius,  and  C  as 
a  center,  draw  the  arc  intersecting  at  F  and  H;  join  AF,  FH 
and  HB,  cctmpleting  the  square  required. 

Fig.  5.  On  a  given  side  AB,  to  construct  a,  regular  Hexagon' 
From  the  points  A  and  B  as  centers,  and  AB  for  a  radius,  des- 
cribe arcs  cutting  each  other  in  C;  and  from  the  point  C,  with 


To  bisect  a  given  angle  sec  Fig.  1,  Plate  3. 


Plate  S.  27 

the  distance  AB,  describe  the  circle  AFB;  then  with  the  dis- 
tance AB,  step  around  the  circumference  the  points  B,  D,  E, 
F,  G;  join  BD,  DE,  EF,  &c.,  for  the  hexagon  required. 

Fig.  6.  On  a  given  line  AB,  to  describe  a  regular  jwhjgon 
of  any  required  number  of  sides.  With  AB  as  a  radius,  and  A 
as  a  center,  describe  tlie  semicircle  BCD,  prolong  AB  to  D, 

If  a  licptagon  (seven  sides)  be  required.  Divide  the  semicircle 
into  seven  equal  parts  as  1,  2,  3,  4,  5,  6,  JB;  from  the  center  A, 
draw  lines  through  the  divisions  6,  .5,  4,  3,  Sea  ,  prolonged,  alw^ays 
omitting  the  la-^t  two  divisions;  with  BA  for  a  radius,  describe 
arcs  from  B  to  C,  and  C  to  ^,  E  to  F,  and  from  Hio  Cr  and  G 
to  F;  join  BC,  CE,  EF,  FG.  HA  and  GH,  and  the  heptagon 
is  complete. 

Any  regular  polygon  maybe  drawn  in  this  way,  the  semicircle 
being  rtivided  otf  C(iual  to  the  number  of  sides  lecfuired  iu  the 
polygon.  The  young  man  will  tind  this  a  good  problem  for  practice  in 
accurate  drawing. 

Fig.  7.  To  consirurt  arqinhir  poI>i<i<>ii,  h<(vinii  ciulit  Kidcs, 
(octagon)  from  a  <iiocn  rUjht  line  AB.  Prolong  AB  to  Cand  D; 
make  AD  aud  BC  each  e<iual  AB;  draw  the  semicircles  A2  D 
and  B  S  C;  draw  arcs  with  equal  radius  from  the  points  jD,  A, 
B,  C,  intersecting  at  E  and  F;  draw  E2  and  F3  perpendicular 
to  DC,  bisecting  the  semicircles  at  3  and  3  ;  join  2  A  and  3  B 
prolonged;  make  AH  and  BJ  each  equal  AB;  draw  AK  and 
BL  indefinite,  and  perpendicular  to  AB ;  draw  iifiV  and  ./M 
each  parallel  with  AK,  and  equal  in  length  to  AB.  From  iVand 
M,  with  radius  equal  to  AB.  draw  arcs  cutting  the  perpendicular 
lines  in  if  and  L;  join  NK,  KL  and  LM.  and  the  octagon  is 
complete.  ^' 

Fig.  8.  A  square  ATiCD,  being  glvoi,  to  form  an  oc(ago7i, 
or  rind  tlir  distance,  from  the  edge  B  to  sri  a  gauge.  Draw  the  diag- 
onals AD  and  BC,  intersecting  at  O,  with  AO  for  a  radius,  and 
A  as  a  center;  draw  the  arc  OH,  then  BH  is  the  required  dis- 
tance from  the  edge  to  set  the  gauge;  draw  arcs  through  the 
center  O,  from  the  four  corners  A,  B,  C,  D,  to  intersect  the 
sides  of  the  .square  at  1,  2,  S,  4,  .5,  0.  7.  Join  Hi,  3  4,  5  6,  and 
7  1,  and  we  have  the  octagon  required. 

A  regular  polygon  of  any  number  of  .sides  may  be  easily 
constructed,  by  first  drawing  a  circle,  and  dividing  the  circumfer- 
ence into  the  nundier  of  parts  reciuired  for  the  sides,  and  then 
joining  the  divisions. 

Fig.  9.  To  divide  a  given  line  AB,  into  any  number  of  equal 
parts.  Let  AB  be  tlie  given  line;  at  A  draw  any  line  indefinite, 
as  AC,  and  at  any  convenient  angle  to  AB;  set  off"  towards  C 
the  number  of  equal  divisions  the  given  line  is  required  to  be 
divided,  as  1,  2,  3,  4,  .5,  (5;  join  6B,  draw  .5  7,  4  8,  3  9,  2  10,  and 
1  II,  parallel  with  6B,  then  the  given  line  AjB  will  be  divided 
proportionately  into  the  number  of  spaces  required. 

Fig.  10.  S/ioirs  the  save  principle  applied,  to  diminishinq 
or  increasing  the  length  of  a  hractict.  Let  AB  be  the  length 
(10^'')  of  the  given  bracket  divided  into  any  number  of  parts,  as 

1,  1,  1,  &c.;  draw  AC e(iual  to  the  depth  of  the  bracket;  draw 
1  2,  1  2,  &c.,  perpendicular  to  AB,  cutting  the  curve  iu  C,  2, 

2,  «&c.;  make  AD  at  any  convenient  angle  to  AB;  make  AD 
equal  the  length  of  the  diminished  or  increased  bracket,  in  this 
case  diminished  to  "1^^.",  join  BD.  From  1,  1,  1,  &c.,  draw  line 
parallel  with  BD,  intersecting  AD  in  3,  3,  3,  «S;c.;  draw  lines 


38  Plate  3. 

indeiinite,  and  perpendicular  to  AD,  from  the  points  A,  3,  3, 
&c.;  make  AC,  3  4,  &c.,  equal  AC,  1  2,  &c.,  respectively; 
then  trace  the  curve  through  the  points  4,  4,  4,  &c.,  for  the 
diminished  bracket  required. 

Fig.  11.  To  divide  a  i/iroi  line  AB,  or  a  hoard  into  any 
tiumhcr  of  equal  divisiotiti.  Let  AJB  indicate  a  board  10'^  wide, 
and  let  it  be  required  to  divide  the  same  into  twenty-one  equal 
parts.  Now  21  half-inches  equal  103.<^';  take  the  rule  or  steel 
square,  place  it  diagonally  across  the  board  to  10}.^  inches  as 
indicated  at  DC,  mark  the  divisions  every  half-inch,  as  1,  2,  3,  4, 
etc.,  draw  lines  parallel  with  D.K,  cutting  the  given  line  AB,  into 
twenty-one  equal  parts  as  required. 

Or  suppose  it  be  required  to  divide  the  same  board  into 
twelve  e()ual  parts,  then  place  the  square  diagonally  across  as 
HJ,  measuring  12  Inches;  then  every  inch  will  be  a  division  on 
the  diagonal  line  JH,  and  lines  drawn  parallel  with  Dif  through 
tiie  divisions,  will  divide  AB  equally  as  required. 

This  problem  is  very  useful  to  draughtsmen  and  mechanics, 
being  a  very  ready  method  of  dividing  any  line  into  a  given 
number  of  equal  parts. 

Fig.  12.  Two  straight  lines  AB  and  BC,  meeting  at  any 
(inijlc  as  ABC  how  to  coniiect  them  with  a  curve  by  intcrsecUiiq 
lines.  Make  BD  and  BE  each  equal,  divide  BD  into  any 
number  of  equal  parts,  as  1,2,  3,  4,  5,  <>;  divide  BE  into  the 
same  number  of  parts,  connect  ID,  \E,  2-5,  &c.,  as  shown, 
and  through  the  intersections  trace  the  easing  required. 

The  stair-builder  sometimes  makes  use  of  this  problem  to 
ease  off  the  angle  on  wall  strings  formed  by  the  level  base  and 
raking  string;  the  distance  BD  or  BE  is  usually  taken  at  two- 
thirds  of  a  tread,  this  is  optional  with  the  workman  as  a  matter  of 
taste. 

Fig.  13.  Shows  tJic  cdshirj  to  br.  an  clliptifal  <-urvt:,  tlic  dis- 
I'lnce  BD  bcini;i  less  than  BE.  Divide  BD  into  any  number  of 
(•<iual  parts,  say  8,  divide  BE  into  the  same  number  of  equal 
parts  1,  2,  3,  4,  5,  6,  7,  8,  &c.;  join  \D,  IC,  3  7,  3  G,  etc.,  and 
trace  the  curve  as  before;  this  easing  is  used  where  the  treads  are 
increased  in  width  at  the  starting  of  a  straight  fliglit  of  stairs,  or 
in  winders. 

Fig.  14.  Shop-s  Jioir  to  find  the  development  or  ^K-^tretc/iont" 
of  a.  fjivcn  semicircle  ABC,  or  any  portion  of  a  semicircle.  Draw 
1)^  indefinite  and  parallel  with  AC,  and  tangent  to  the  curve  at 
B;  then  with  AC  for  a  radius,  and  A  and  C  for  centers,  draw 
arcs  intersecting  at  J^;  join  FA  and  FC  prolonged,  intersecting 
DE  at  D  and  E;  then  the  length  of  the  straight  line  DE  is 
c<iiial  to  the  circumference  of  the  semicircle  ABC  nearly. 
Any  division  of  the  semicircle  may  now  be  found  from  the 
stretchout.  Make  BH  equal  i^  inches;  join  FH,  intersecting 
the  semicircle  in  J,  then  the  distance  from  B  to  J,  on  the  curve, 
will  equal  4^4  inches;  in  like  manner  any  number  of  divisions 
may  be  found.  The  distance  BD  or  BE,  equals  the  stretchout 
of  the  quadrant  AJB.  If  the  stretchout  of  the  quadrant  only  be 
required,  then  with  OC  for  a  radius,  and  the  points  O  and  Cfor 
centers,  draw  arcs  intersecting  at  L\  draw  LC  prolonged  to  E, 
then  BE  is  the  development  of  the  curve  from  B  to  C 


Pl-ATB  4.  29 

PLATE  4. 

Thk  Cone. 

Pig.  1.  Exhibits  a  "  riifht  coiie,"  and  is  defined  as  being 
generated  by  the  revolution  of  a  rUjht  angle  triangle  around  one 
of  its  sides,  that  forms  the  right  aiujle,  and  is  tenaed  a  ^^  circular 
co7ie,"  A  line  from  the  apex  JB,  to  the  center  A,  is  termed  its 
"ftxis."  In  "oblique"  cones,  the  axis  is  inclining  to  the  plane 
of  base  CD,  at  an  angle  other  than  a  right  angle.  A  ''truncated" 
cone,  is  the  lower  part  of  a  cone  cut  by  a  plane  parallel  to  its 
base. 

Conic  Sections.  Four  curves,  called  conic  sections,  may  be 
found  by  cutting  the  right  cone  in  different  directions.  If  the 
cone  be  cut  by  a  plane  parallel  to  its  base,  as  JSF,  the  section  is  a 
''circle  ;"  if  the  plane  cut  the  cone  from  side  to  side,  as  GH,  and 
at  any  angle  other  than  a  right  angle  to  its  axis,  the  section  is  an 
"ellipse" as  shown  projected  at  Fig.  3;  if  the  cutting  plane  be 
parallel  to  one  side  of  the  cone,  as  the  line  JK,  the  section  will  be 
a  "  parabola,"  as  shown  projected  at  Fig.  4;  again,  if  the  cutting 
plane  be  parallel  to  the  axis  AB,  as  LM,  then  the  section  will  be 
a  "hyperbola,"  as  shown  projected  at  Fig.  5. 

To  find  the  superficial  area  of  the  slariting  side  of  a  right  cone: 

EULE.— Multiply  the  diameter  by  the  constant  3.1416,  and  that 
Droduct   by   oue-balf   tlie   slant   height   for   the    superficial    area. 


To  compute  the  cubic  feet  of  a  right  cone: 

Rule.— Multiply  the  square  of  the  diameter  by  the  decimal  .7864; 
then  multiply  that  sum  by  the  perpendicular  height,  and  take  one- 
third  of  the  product  for  the  area  required.  Example:  Required  the 
area  In  cubic  feet  of  a  right  cone,  the  diameter  at  the  base  is  16'  0", 
and  the  perpendicular  height  equals  24' 0".  Thus,  16'xl6'=256x.7a54= 
201.062  square  feet  for  the  superficial  area  of  the  base.  Then,  201.062 
X24'0"=4825.488-^}3=1608.496  equals  1608.4969  cubic  feet  for  the  area 
required. 

Fig.  2.  Shows  the  base  of  the  cone ;  the  shaded  part 
marked  B,  indicates  the  base  of  the  parabola,  and  the  shaded 
part  marked  C,  indicates  the  base  of  the  hyperbola. 

Fig.  3.  Shows  the  ellipse  projected  from  the  plane  GH,: 
Fig.  1.  How  to  locate  the  minor  axis  and  trace  the  curve. 
Return  to  Fig.  1,  bisect  GH  at  N,  through  N,  and  parallel  to  the 
base  CD;  draw  EF,  cutting  the  axis  AB  at  O,  with  O  as  a 
center  and  OF  for  a  radius;  draw  the  arc  cutting  the  perpendic- 
ular from  N  at  P;  then  NP  is  the  semi  minor  axis  sought. 

Make  GH  equal  GH,  Fig.  1;  make  JVPand  iVC  equal  NP, 
Fig.  1 ;  draw  the  rectilineal  parallelogram  GHAB,  divide  HA 
into  foar  equal  parts,  as  1,  2,  3  ;  also  divide  NH  into  four  equal 
parts,  as  4,  .5 .  6.  From  the  focus  P.  draw  the  intersecting  lines 
P  1.  P  2,  P  3 ;  from  the  focus  C,  draw  lines  through  the  points 
4,  5,  6,  to  intersect  at  7,  8,  9,  for  the  one-fourth  of  the  ellipse. 
Now  draw  the  ordinates  8-10.  9.11  parallel  to  the  minor  axis 
CP ;  divide  GN  to  equal  NH ;  now  transfer  the  distance  on 
ordinates  6-8,  5-9  to  the  opposite  sides,  using  the  transverse  axis 
GH  for  a  base  line,  then  trace  the  elliptic  curve  through  the 
points,  for  the  ellipse  required. 


90  1*LATE  4. 

Fig.  4.  Shrnos  the  curve  of  a  Parabola  projected  from  the 
plane  JK,  FUj.  1.  Make  DE  equal  to  DE,  Fig.  2  ;  bisect  DE  at 
K,  draw  KJ  perpendicular  to  DE.  and  equal  to  KJ,  Fig.  1; 
draw  the  rectilineal  parallelogram  DFGE,  divide  KE  into  four 
equal  parts  as  1,  2,  3  ;  divide  EG  into  four  equal  parts,  as  4,  5,  6; 
connect  J  6,  J  5  and  J"  4  ;  from  the  points  1.  2,  3,  draw  lines  par- 
allel to  KJ  to  intersect  the  lines  from  the  focus  J,  at  7,  8  and  9. 
Now  divide  the  opposite  side  in  the  same  manner,  and  trace  the 
parabolic  curve  through  the  points  E,  7,  8,  9,  J,  10,  11,  13,  D. 

Fig.  5.  Shows  the  curve  of  a  Hyperbola,  projected  from 
the  plane  LM,  Fig.  1.  Make  FG  equal  to  FG.  Fig.  2  ;  bisect 
FG  at  M,  draw  ML  perpendicular  to  FG  and  equal  to  ML.  Fig. 
1  ;  draw  the  rectilineal  parallelogram  FBAG  \  divide  AfGr  into 
four  equal  parts,  as  1,  2,  3,  divide  GA  into  four  equal  parts,  as 
4.  5,  6  ;  connect  i  6,  i  5  and  L  4.  Prolong  the  side  of  cone 
DB,  Fig.  1  to  intersect  ML  prolonged  at  R.  Now  prolong  ML, 
Fig.  5,  to  equal  MR,  Fig.  1  ;  at  i?  draw  R  1,  Rl  and  i?3,  inter- 
secting iJ4,  i5  and  ie  at  7,  8  and  9 ;  divide  the  opposite  side 
in  the  same  manner,  and  trace  the  Hyperbolic  curve  through  the 
points  G,  7,  8,  9,  L,  10,  11,  13,  and  F. 

Fig.  6.  Shows  how  to  draw  a  pattern  for  the  turner,  to 
iurn  a  circular  moulMng  for  a  given  moulding,  and  lutve  them 
'member  on  a  given  miter.  A  shows  the  given  moulding,  and 
BC  shows  the  given  miter;  draw  lines  from  the  different  mem- 
bers on  moulding  to  intersect  the  miter  BC  at  1,  2,  3,  4,  5.  From 
the  center  O  draw  arcs  from  the  points  1,  2,  3,  &c.,  on  the  miter, 
to  intersect  the  radial  line  OD;  then  transfer  the  ordinates  on  the 
given  moulding  to  Fig.  7,  as  G-7,  drawn  at  right  angles  to  DO; 
then  trace  the  contour  of  moulding  to  be  turned,  through  the 
points,  for  the  pattern  required.  If  the  circular  moulding  is 
turned  to  the  exact  pattern  of  the  given  moulding,  then  the  miter 
will  be  curved,  as  shown  at  Fig.  8. 

At  AB  and  C,  Fig.  8,  is  shown  the  intersection;  now  draw  the 
curve  through  the  three  points,  as  described  for  Fig.  8,  Plate  3, 
for  the  miter. 

Fig.  9.  Shows  Graphically  how  to  find,  approximately  the 
number  of  feet  of  loreath  rail  in  a  tvinding  stair  case  -when  esti- 
mating. 

The  diameter  of  well  hole  is  4''  0^\  and  the  height  of  story 
is  12^  0^^,  having  24  risers  in  one  revolution. 

EUT.E.— To  the  .square  of  the  heigrht  add  the  square  of  three  times 
the  diameter  of  well  hole,  and  extract  the  square  root  for  the 
lippothenuse,  or  leugth  of  wreath  rail  approximately. 

Example.— 12'X12'=144-^  [4'  0"X3=13'0"Xl2'  0"=144'1  144+144=  /288= 
17'  0"  for  tlie  length  of  the  wreath  rail  approximately. 

For  the  correct  measurements,  first  find  the  exact  circumfer- 
ence, then  proceed  as  before. 

Rule.— To  find  the  circumference,  multiply  the  diameter  by  the 
constant  3.1416. 

Example.-^'  0"X3.1416=12.56(>4;  equals  12.5664  for  tlie  circumference 
of  well  hole.  Then  proceed  as  above.  12X12=144+12.566X12.566= 
■l/301,904a'56=17.35  feet;  which  equals  17.35  feet  for  the  exact  length  of 
weath  rail  at  the  cylinder  line. 

If  the  ground  plan  be  elliptic(d,  then  find  the  circumfer- 
ence by  the  rule  for  the  ellipse,  and  proceed  aa  above. 


Plate  5.  81 

PLATE  5. 

The  Ellipse. 

Plate  5.  Shoivs  the  Ellipse,  AB,  Fig.,  1  is  the  Transverse 
Axis,  and  is  commonly  termed  the  Major  Axis,  for  short. 

The  Conjuiiate  Axis  is  the  short  axis,  as  CD,  Fig.  1,  bisect- 
ing the  Major  Axis  at  right  angles  and  terminated  by  the  curve  ; 
it  is  termed  for  short  the  Minor  Axis.  Foci,  are  two  points  found 
on  the  major  axis  as  J  and  K,  Fig.  2,  from  which  to  draw  the  cir- 
cumference with  a  string ;  the  two  points  together  are  termed  the 
Foci;  singly,  one  is  termed  Focus. 

Vectors  are  the  two  lines  that  radiate  from  any  point  in  the 
circumference  to  each  of  the  foci  as  DJ  and  DK,  or  LJ  and 
IjK,  Fig.  2.  It  is  a  known  property  of  the  ellipse,  that  the  sum 
of  the  two  vectors  is  equal  to  the  transverse  diameter. 

Center.  The  center  of  the  ellipse  is  at  the  intersection  of  the 
axis,  as  at  F,  Fig.  1. 

Vertix.  Is  the  extremity  of  the  axis,  as  at  the  mixed  angles 
at  ABC  and  Z),  Fig.  1. 

Nm~mal.  The  axis  AB  and  CD  are  always  normal  to  the 
curve  at  their  Vertices.  To  find  a  line  normal  to  the  curve  at  any 
intermediate  point,  bisect  the  vectors  at  the  circumference,  as 
shown  by  the  line  1  2,  Fig.  8,  which  is  normal  to  the  curve  at  the 
point  H. 

In  this  way  the  mason  finds  the  joints  for  the  arch  stones  in 
elliptical  arches  at  any  point  desired. 

Tcmgent.  Any  line  at  right  angles  to  the  normal  at  the  point 
of  contact  with  the  curve  will  be  tangent  to  the  curve  at  that 
point,  as  the  line  3  4,  Fig.  8. 

Scmi-cllipsc.  Both  the  axis  divide  the  ellipse  into  two  parts, 
as  ADBA,  or  CBDC,  either  are  termed  semi-ellipsis ;  the  area 
is  the  same  in  either  case. 

Elliptical  Quadrants.  The  same  axis  divides  the  ellipse  into 
four  equal  parts,  termed  elliptical  quadrants,  all  having  the  same 
area,  as  CFBHC,  Fig.  1. 

Rule.*— To  ^nd  the  circumference  of  an  ellipsis,  the  major  and  minor 
axis  being  known.  Multiply' half  the  sum  of  the  two  diameters  by 
iJ,1416,  and  the  product  will  oe  the  circumference  nearly. 

Example.— The  major  axis,  Fig.  1,  equals  14'  0",  and  the  minor  axis 

24  5 
equals  Ity  6".  required  the  circumference:  W.O+Ky.S-^-^^  =12.25'X3.141C 

=38,484  feet,  answer. 

Rule —To  find  the  area  of  an  Ellipse.  Multiply  tlie  major  axis 
by  tlie  minor  axis  and  the  product  again  by  the  decimal  .7854,  and  the 
result  will  be  the  area. 

Example.— 14' (yx'lO.SX. 7854=115.453  square  feet,  answer. 

Fig.  1.  Shows  how  to  draw  the  ellipse  with  a  trammel,  the 
imijor  axis  AB,  and  mi)wr  axis  CD,  being  given.  Pivot  the 
trammel  in  the  center  at  F,  with  the  arms  centered  on  the  axis 
lines  AB  and  CD. 

Make  the  distance  from  pencil  to  minor  pin  equal  the  semi- 
minor  axis  CF^,  and  the  distance  from  pencil  to  major  pin  to  equal 
the  semimajor  axis  AF;  now  place  the  pins  in  the  grooves,  and 
trace  the  curve  through  the  points  ACBD,  for  the  ellipsis  required. 

The  trammel  is  the  most  practical  tool  for  the  Stair  builder  to 
trace  the  curves  of  the  face  mould,  especially  for  platform  cylinders, 
say  up  to  24  inches  diameter;  tlie  elliptic  curve  can  be  more  correctly 
traced  with  the  trammel  than  in  any  other  way,  the  curve  being 
absolutely  correct. 

♦Boueycastle's  Mensuration. 


33  Plate  5. 

The  Stair  builder  snould  not  consider  his  kit  complete  iinless  pro- 
vided witli  a  trammel.  For  platfoiui  cylinders  up  to  the  size  above 
mentioned,  the  arms  of  tlie  trammel  need  not  be  longer  tlian  7  inches 
each,  and  the  rod  not  over  20  inches  long,  and  14"  ^tiuare,  having  at 
the  end  a  head  drilled  out  to  admit  a  pencil,  and  a  set  screw,  to  secure 
the  pencil  in  place;  also,  two  movable  heads,  with  set  screws  and 
pins,  the  pins  may  be  one-sixteenth  in  diameter,  to  fit  neatly  into  the 
grooves  of  the  trammel;  these  two  Jieads  are  fit  so  as  to  slide  easily 
on  the  rod,  tlioy  are  V-z"  by  ?i"  square,  and  the  set  screws  should  be  on 
the  opposite  side  from  the  pins,  for  convenience,  when  setting  them. 

The  first  pin  from  the  pencil  is  termod  the  mmor  pin;  the  other  is 
termed  the  major  jjin. 

At  Fig,  1,  the  trammel  is  shown  having  four  arms;  for  ihe  Stair 
builders'  use,  only  three  arms  are  I'equired,  made  U"  thick  ami  V2" 
wide,  with  grooves  at  right  angles  and  a  scant  eighth  of  an  inch  deep, 
and  a  strong  sixteenth  wide,  so  that  tlie  pins  may  slide  freely  in  the 
grooves ;  have  at  the  center,  on  the  underside,  a  small  point  for  a  pivot 
for  centering  the  tramme]. 

This  instrument  sliould  be  made  of  brass.  After  using  the  tool  for 
a  short  time,  tlie  Stair  builder  would  not  be  without  it.  The  author  lias 
used  the  trammel  on  platform  cylinders  for  tlie  last  forty  years. 
For  winders  and  large  curves  the  ordinate  as  lierein  set  fortli  is  found 
to  be  the  most  convenient  for  economy  in  drawing  a  correct  face 
mould. 

Fig.  2.  A  rectilineal  parallelogram,  1,  2,  3,  4,  being  given, 
tn  find  tlie  major  and  minor  axln,  (duo  the  foci,  and  draw  the 
cUipnis  UHth  a  string,  so  that  tlic  curve  irill  he  tangent  to  the 
parallelogram  at  tlie  points  A,  S,  C  and  D. 

Bisect  1  3  and  2  4  at  A  and  B,  also  bisect  1  2  and  3  4  at  C 
and  D,  join  A  B  and  CD,  forming  right  angles  at  the  center  F; 
then  AB  will  be  the  major  axis  and  CD  the  minor  axis  required. 
With  the  scmimajor  axis  AF  for  a  radius,  and  J?  as  a  center,  draw 
the  arc  intersecting  the  major  axis  AB  at  J  and  K ;  then  the 
points  J  and  K  will  be  the  foci  required. 

Now  fasten  a  pin  in  each  focus  J" and  K,  pass  a  thread  around 
the  pins,  wrapping  the  two  ends  twice  around  tlie  one  pin,  and 
liolding  the  ends  under  the  thumb  of  the  left  hand,  then  with  a 
pencil  nicked  slightly  near  the  point,  stretch  the  thread  until  the 
point  D  is  reached  ;  now  trace  the  curve  through  the  points 
DBCA  for  the  olliiisis  required. 

Fig.  3.  Around  a  given  rectangle,  ABCD,  to  describe  an 
ellipsis. 

Bisect  AC  and  BD  at  J57and  F,  join  JE7  and  J' and  produced; 
bisect  AB  and  CD  at  iifand  J.  Join  HJ,  intersecting  EF  &i  the 
center  O.  Make  HK  equal  HB,  join  KA.  cutting  EF  at  M. 
Then  AiT  will  e(|ual  the  .semimajor  axis,  and  AJkfthe  semiminor 
axis.  Make  OiVaud  OF  each  ecju.al  KA.  Let  OR  and  OS  each 
o(iual  AM;  now  trace  the  elliptic  curve  through  the  points 
ABCD,  as  required. 

Fig.  4.  An  Ellipsis,  ABCD,  having  been  given,  and.  the 
position  of  the  major  (tnd  minor  ((.ris  is  nnknoum,  to  find  their 
posUimi. 

Draw  any  two  parallel  lines  cutting  the  ellipse,  as  AC  and 
BD.  Bisect  AC  and  BD  at  1  and  2,  Join  1  2  produced  to  inter- 
sect the  ellipse  at  J57and  F;  bisect  EF  At  H;  tlien  the  point  at  3 
will  be  the  center  of  the  ellipse.  With  any  radius  less  than  the 
semimajor  axis,  and  3,  for  a  center,  draw  tlie  arc  cutting  the 
ellipse  at  iJ"  and  J,  join  HJ ;  tlirough  the  center  3,  draw  the 
minor  axis  KL,  parallel  with  HJ.  Bisect  HJ  at  4,  join  4  3  and 
produced,  cutting  the  ellipse  at  M  and  N,  for  the  major  axis,  as 
required. 


Pl.ATK  5.  33 

Fig.  5.  To  drwv  an  elUjJse  or  ovid,  ABCD,  ivith  the 
dividers,  the  majnr  cixii^  AC  being  rjivcn. 

Let  AC  be  the  major  axis,  divide  the  same  into  four  equal 
parts,  as  A  3,  3  3,  3  1,  1  C.  Make  the  two  middle  parts  equal  the 
diagonal  of  tlie  square  1-6,  3-7  ;  prolong  the  sides  of  the  square 
at  1  and  3  indefinite  ;  theu  with  3  as  a  center,  and  3  A  for  radius, 
draw  the  arc  FAE.  Also  from  the  center  1,  draw  the  arc  HCJ, 
then  with  7,  as  a  center  and  7  H  for  a  radius,  draw  the  arc  H13F. 
in  like  manner,  from  the  center  6,  trace  the  opposite  side  ED  J, 
and  the  ellipse  or  oval  is  complete. 

Fig.  6.  An  Ellipse  shorcn  hy  the  dotted.  Vme  3,  3,  4,  .5,  heluu 
(jiven;  to  draw  other  lives  tJiat^cill  he  pandlcl  to  the  fjiven  ellipse: 
3  4  is  the  major  o.rf.v,  and  3  5  tlic  iiiitior  axis. 

Draw  eqaal  arcs  on  each  side;  of  the  given  ellipse  to  the 
required  width,  then  trace  the  cur\Ts  so  as  to  tangent  the  arcs,  for 
the  parallel  lines  required  as  ABCD,  for  the  convex  curve;  and 
JEHF  for  the  concave  curve.  If  a  ]>attern  be  required,  tra<'e 
eitlicr  of  the  outer  curves,  theu  use  a  gauge  for  the  parallel  width. 

Fig.  7.  An  Ellipse  ABCD  being  given;  to  draw  another 
ellipse  EFGH,  tJirnngh  agloen  point  F,  that  shall  be  propor- 
tujnul  to  the  given  ellipse. 

Let  ABCD  be  the  given  ellipse,  AC  tlie  major  axis  and  BD 
the  minor  axis,  aud  O  tlic  center,  and  JPiJ  tlie  minor  axis  for  the 
jMoportlonal  ellipse.  Join  AB,  from  F,  aud  pai-allel  to  the  dotted 
hue  AB,  draw  the  proportional  Iiii<!  FJE.  Make  OG  equal  OE, 
for  the  major  axis.  Now  trace  the  ('llii)tlc  curve  througJi  the  ])oiids 
EFGH,  which  will  be  proportioual  to  the  given  ellipse,  as  reiiuiied. 

If  any  line, orliues,  be  diiiwn  radiatinpf  from  the  center  O  to  tlic^ 
cirrniiiferenccof  the  i^iven  ellipse,  as  0  2,  O.J,  or  0  4;  the  width  of  any 
con(;putrlc  or  proportional  ellipse  may  be  established  at  any  of  theso 
points  by  the  use  of  tiie  proportional  lines.  Say  draw  A  2.  then  draw 
rJ  .'>  p;irallel  to  A  2,  now  5  is  the  point  t  hrough  whicli  the  proportional 
r-llipsc  will  cut  on  tlio  radial  line  O  ?.  In  the  same  way  draw  other 
proportional  lines,  as  2  D,  D3,  and .'{  C,  &c.,  parallel  to  which  draw  5H, 
Jlfi,  and  6  G ;  then  trace  tbo  tdliptii;  curve  and  it  will  be  found  to  pass 
tbrouj;h  the  points  •'«,  JJ,  6',  &o.  Tliosii  proijortional  lines  are  some- 
times found  useful  when  drawing  tlio  face-mould. 

Fig.  8.  To  dram  a,  line  perpcndicidar,  or  normal  P)  the 
cui^e  of  a  giv(n  Ellipse;  also  to  find  a,  tangent  to  tlie  same  curve. 

Ijct  ACBD  be  the  given  ellips*; ;  jiud  the  jioint  H  be  selected 
for  the  line  noniial  1o  the  curve  ;  liud  the  foci  E  and  F,  drav/  th?' 
vectors  EH,  andJ^iif  pi-oduced  ;  bisect  the  iuigle  formed  at  H,  and 
draw  the  normal  line  1  2,  which  will  lie  j>erpeudicular  to  the  curve 
of  the  ellipse  at  tlie  ]ioiut  H,  a.s  recpiired. 

At  the  point  H,  and  at  light  angles  to  1  3,  draw  the  line  3  4  ; 
then  3  4  will  be  tangent  to  the  ellipse  at  the  point  H.  Another 
way,  to  find  a  tangent  to  the  curve:  Let  the  vectors  converge  at  the 
])oint  J'and  piolong  indeliuitely.  Bisect  the  angle  in  K,  join  KJ, 
then  the  line  KJ  will  be  tangent  to  the  ellipse,  and  the  point  of 
contact  will  be  at  J. 

Fig.  9.  A  SonieUipse  ABC,  bring  given  to  find  a,  titngent 
to  the  enrvi'  at,  avg  point  ivitliout  the  foci. 

JiQt  AB  be  the  major  axis,  and  O  the  center,  and  OC  Ibn 
semiminor  axis  produced  to  H.  l^rav,'  the  quadrant  and  radii  OD 
and  CF ;  perpendicular  to  Oi^d raw  .FiJ,-  draw  J^J"  parallel  with 
OB,  join  iJJ"  and  produced,  for  the  tangent  required,  the  point  of 
contact  is  at  J ;  the  tangent  KL  is  found  in  the  same  way,  K 
being  the  point  of  tangency. 

If  the  curve  of  the  ellipse  is  not  given,  the  point  of  langency 
may  be  found  by  taking  the  radius  OA,  and  O  for  a  center,  draw 


84  Ti-ATE  5. 

the  arc  cuttius  OD,  inixluced  in  M,  from  M  draw  the  per]ipi)dic'- 
ular  cuttiug  KD  iu  K,  theu  the  point  K  will  be  the  point  of 
contact. 

Fig.  10.  The  radius  of  any  Quaitcv  Circle,  and  its  nccoin- 
panying  Rhomhoidal  parallelogram  ABCD,  being  given;  how 
to  trace  tlic  curve  of  an  Ellipse  ivith  a  trammel  fhrongJi  the 
jjoints  A  and  C,  so  that  AB  and  BC  shall  be  tangent  to  the, 
curve  at  the  points  A  and  C;  and  at  the  satnc  time  locate  the 
position  of  the  major  and  minor  axis,  the  length  of  the  7najor 
cuyis,  and,  position  of  both,  major  and  minor  axis  being  roiknoini. 

Pivot  the  trammel  in  the  point  D;  set  from  pencil  to  minor 
pin  the  distance  eqnal  to  the  radius  DL,  of  quarter  circle,  (whidi 
is  always  etpial  to  the  length  of  the  semi-minor  axis  of  its  accoiii- 
panyins?  ellipse).  I'lace  the  pencil  in  the  point  C,  and  tlui  minor 
pin  iu  the  groove  at  F,  and  the  major  pin  iu  the  groove  at  H;  now 
slightly  fasten  the  major  pin,  and  move  the  rod  to  the  point  A. 
holding  the  tranuiiel  firmly.  If  the  pencil  reaches  beyond  the 
point  A,  slide  the  major  pin  closer  to  the  minor  pin,  and  fastm 
again,  also  move  the  trannnel  a  little,  and  try  again,  nutil  the  jx-nci! 
will  pass  through  the  point  AC.  Then  fasten  securely  the  major 
piu,  and  trace  the  elliptic  cur\e  KCAJ,  as  required. 

The  position  of  the  tranmiel  now  gives  the  direction  of  the 
major  axis  JK,  also  the  minor  axis  DL,  and  the  pencil  describes 
the  elliptic  curve.  FC  efpials  the  length  of  semi-minor  axis,  and 
JETC  equals  the  length  of  semi-major  axis,  and  the  sides  AB  and 
BC  of  the  Rhomboid  are  tangent  to  the  cune  at  the  points  A  and 
C,  as  required. 

Fig.  11.  ThUi  problem  is  the  same  as  the  preceding  for  the 
center  ellipse,  and  is  intended  that  proportional  lines  A  L,  L  o, 
SC,  CK,  aivd  their  parallels,  maybe  drawn,  giviny  the  width  of 
concentric  ellipses  at  the  points  A,  L,  3  C,  and  K. 

The  radius  of  any  circle,  as  has  been  stated,  always  ecjuals  the 
semi-minor  axis  of  any  accompanying  ellipse.  Theu  DL  equals  tli<> 
length  of  the  semi-nuuor  axis  :  and  A  is  anotlier  fixed  i>oint  at  the 
end  of  the  parallelogram  ;  C,  at  the  opposite  end,  is  another  fixed 
point,  that  the  curve  has  to  pass  through:  on  the  diagonal  line  DB 
anotlier  point,  o.  may  l>e  estal)lished  ;  the  method  to  establish  this 
point  is  shown  at  Fig.  4.  Tlate  24  ;  also  Fig.  2,  Plate  o2.  Now 
joiu  LA,  Lo,  3  C.  CK.  Make  1,2,  1.2.  each  equal  hall  tho 
thickness  of  the  cylindri<;  section.  Draw  2  4  parallel  with  AL, 
also  2  5,  5  6,  0  7,  parallel  with  the  renter  proportionals,  intersect- 
ing the  radials  DB,  DC,  DK  aixl  DA.  At  these  intersectioiis  the 
points  are  given  through  which  the  cuiwes  will  pass,  a  pliable  .strip 
nmy  l»e  used  to  trace  the  curve  through  the  points,  instead  of  the 
trammel. 

A  line  that  will  be  nonnal  to  the  curve  at  the  point  A  is  drawn 
at  right  angles  to  the  tangent  AB  as  PS. 

At  Can  inrlefinite  amount  of  straight  wood  maybe  added 
parallel  to  BC  prolonged  fiom  the  points  6,  6. 

Fig.  12.  tihows  horn  the  Ellipse  may  be  drawn  with  a 
straiyht^cdgc,  and  a  pliable  strip. 

Let  AB  indicate  the  major  axis,  and  CD  the  length  of  the 
minor  axis,  and  O  the  center  of  the  ellipse,  required  ;  let  EF  indi- 
cate the  straight-edge.  Make  a  nick  at  H ;  make  i?J  equal  OC ; 
let  HK  equal  OA  ;  now  move  the  rod  at  intervals,  keeping  the 
poiuts  J  and  K  directly  over  the  axis  lines,  and  marking  points  at 
the  nick  H,  as  2,  3,  <Src.,  then  trace  the  elliptic  cm-ve  through  the 
points,  using  a  pliable  strip.* 

*  Mr.  Russell  Iihs  applied  this  method  to  describing  the  elliptic 
curves  of  the  face-mould. 


Pi.ATJC  6.  35 

PLATE  6. 

TlIK    8ci!OM.. 

Exhibits  how  to  draw  the  Scroll. 

Fig.  1.  [Scale,  Z'^  equal  1  foot.]  Shows  Juyw  to  draw  the 
Scroll  by  qundraiUs. 

Let  AB  indicate  the  full  width  of  scroll  from  out  to  out. 
Divide  AB  into  eight  equal  parts  ;  bisect  AB  at  C.  drop  half  a 
space  to  D ;  pen)endicular  to  AB  di-aw  DF,  equal  to  a  whole 
space  ;  bisect  DF  at  O ;  with  O  as  a  ceuter.  and  OB  as  a  radius, 
draw  the  semicircle  from  D  to  F.  Make  AE  equal  a  space,  draw 
the  diagoual  EB  intersecting  the  semicircle  at  H,  draw  FH  and 
DH  indefinite.  From  F,  and  at  right  angles  to  FD,  draw  FJ, 
and  at  right  angles  to  FJ  draw  JK,  and  at  right  angles  to  JK 
draw  KL,  &c.,  establishing  the  points  D.  F,  J,  K,  L  and  M, 
from  which  to  draw  the  scroll  by  quadrants. 

With  D  for  a  ceuter,  and  IDB  as  a  radius,  draw  the  cun-e  to 
intersect  Z>i?' prolonged  at  N ;  again,  with  J*  for  a  center,  and  JF'JV 
as  a  radius,  draw  the  curve  to  intersect  JFV  prolonged  at  E.  Pro- 
ceed in  like  manner  to  draw  the  other  quarter  circles  F,  Q,  R  and 
S.  Make  ST  equal  the  width  of  rail,  and  draw  the  inside  curves 
in  like  manner.     Draw  the  shaidc  B  Vat  right  angles  to  BA. 

It  will  be  observed  that  any  number  of  revolutions  may  be 
drawn  in  this  w^ay  ;  the  shank  may  be  drawn  at  either  of  the  quad- 
rants. From  S  around  to  E  is  termed  one  revolution,  and  from  E 
around  to  B,  is  half  a  revolution.  Draw  the  eye  of  scroll  from 
tlie  center  H. 

Fig.  2.  [Scale,  half  size.]  Shows  how  to  find  the  centers 
from  whi^h  to  draw  the  Scn/U,  draicn  half  size,  and  lujrees  with 
Fig.  1.  the  lettering  being  the  .sa»/u\ 

Fig.  3.  [Scale,  K^^=l  foot.]  Shows  the  ^vidth  of  Scroll 
AB,  divided  into  seven  equal  parts.  The  centers  from  whifh  to 
draw  the  quadrants,  are  found  precisely  the  same  way  as  at 
Fig.  1. 

Fig.  4.  [%^^  scale.]  Shows  the  curtail  step,  and  is  drawn 
from  the  same  centers  as  Fig.  3  ;  Sis  the  Block,  and  is  cut  out  to 
the  shape,  from  a  thick  piece  of  very  dry  stuff,  the  depth  of  the 
rise  less  the  thickness  t)f  step.  R  is  tlie  rise,  which  is  shouldered 
at  W;  Vis  the  veneer,  and  is  reduced  at  Wto  a  scant  eighth  of 
•Ml  inch,  and  is  still  fnrtlier  reduced  tapering  towards  the  end  at 
K,  to  a  sixteenth  of  an  inch.  A  kerf  at  K,  is  shown  for  the 
xeneer  to  enter.  Folding  wedges  are  shown  at  W,  to  be  entered 
from  l)Oth  sides  at  the  same  time,  to  strain  the  veneer  to  place 
eveidy  ;  iS  shows  the  outer  string,  and  the  concave  side  of  block  is 
shown  vene(Med  to  match  the  string.  This  may  not  be  necessary, 
unless  tlie  outer  string  be  of  some  fancy  wood ;  N  shows  the 
nosings  of  steps. 

1  Let  it  be  observed,  that  by  dividing  the  width  of  scroll  into  a 
greater,  or  less,  number  of  spaces,  the  revolutions  will  be  closer 
together,  or  open,  as  the  case  may  be. 

The  line  EB  will  pass  througli  the  center  H,  and  the  two 
lines  FK  and  DJ  will  fonn  right  angles  at  H. 

Fig.  5.  [Scale,  IK '^=1  foot.]  Exhibits  a  reciprocal  Scroll, 
draxvn  by  segnients. 

Draw  AJB  and  CD  to  fonn  the  four  right  angles  at  O  ;  divide 
each  right  angle  into  four  equal  parts,  and  draw  the  radial  lines 


S6  Pr>ATE  7. 

through  the  center  O  indefinite.  Draw  the  eye  of  soroll  at  O;  from 
the  verge  of  eye,  draw  tlie  cliord  2  3  at  right  angles  to  O  2  ;  from 
the  point  3  tiraw  tlie  chord  3  4  at  right  angles  to  O  3  ;  from  the 
point  4  draw  the  chord  4  5  at  riglit  angles  to  O  4.  Proceed  in  this 
way  on  each  radial  line,  until  a  sufficient  number  of  revolutions 
are  laid  olf.  Then  connect  the  points  2  3,  3  4,  4  5,  &c.,  by  seg- 
ments, in  this  manner.  With  O  31  for  a  radius,  and  31  for  a 
ceutei-,  draw  arc  at  JT,  with  the  same  radius  and  point  32  I'oi-  a 
center;  draw  arc  intersecting  at  jP.  Thi'u,  with  F  for  a  center, 
draw  the  arc  from  31  to  32.  Again,  with  O  30  for  a  radius,  and 
point  30  for  a  center,  draw  arc  at  H,  with  the  same  radius  and 
point  31  for  a  center,  draw  are  intersecting  at  H,  then,  with  H 
for  a  center,  draw  the  arch  from  30  to  31. 

In  like  manner  find  point  J,  and  othei'S,  from  which  to  com- 
plete the  spiral  line  tor  the  convex  curve  of  pattern.  Draw  the 
concave  side  DLN,  also  the  center  line  MP,  parallel  to  the  convex 
curve.  The  straight,  or  wreath  rail,  may  connect  the  scroll  at  any 
point  in  the  cnr\'e,  at  rigirt  angles  to  the  radius  of  any  segment. 

This  scroll  has  a  beautiful  effect  at  the  starting  of  a  winding 
flight  of  stairs ;  a  ground  plan  made  for  winders  to  conform  to  this 
mixed  curve,  the  result  will  be  a  very  gracefnl  twist. 

Figs.  6,  7  and  8.  [Scale,  one-half  full  size.]  Shows  how 
to  find  the  contour  of  a  Mouhlcd  Cap,  from  a  given  section  of  rail, 
so  the  timber  may  turn  the  cap  to  suit  the  profile  of  rail. 

Fig.  6.  Shows  a  section  of  Hand-rail  S^^^X^M^'- 
Draw  the  parallelogram  ABCD,  for  the  half  section  of  rail. 
Divide  BCinto  any  number  of  parts,  as  1,  2,  3,  4,  &c. ;  draw  SA 
indefinite  ;  anywhere  on  JBA  prolonged,  say  O,  Fig.  7.  Draw  OJE 
at  right  angles  to  OB,  and  equal  to  the  radius  of  newel  cap,  say 
4^''.  Then  with  OE  for  a  radius,  and  O  as  a  center,  draw  the  cir- 
cumference of  cap,  intersecting  OA  at  F ;  make  FG  equal  to  half 
width  of  rail  BCf ;  prolong  CI?  to  intersect  the -circumference  of 
cap  at  JET,  connect  G^Jif  for  one  side  of  miter.  Parallel  with  GB, 
and  from  tlie  points  1,  2,  3,  <fee.,  draw  lines  cutting  the  contour  of 
rail  section  at  0,  0,  0,  and  to  intersect  the  miter  GH  at  1,  2,  3,  iVrc. 

Fig.  7.     Slioios  the  Miter  into  the  Cap,  Fig.  S. 

From  the  center  O,  carry  the  points  1,  2,  3,  &g.,  on 
GH  to  KE,  Fig.  8.  Make  EQ  equal  AB,  for  the  thickness  of 
cap.  Now,  transfer  1  0,  2  0,  3  0,  also  J*  0,  iVO,  &c.,  from  Fig.  Ci 
to  corresponding  lines,  Fig.  8,  then  through  the  points  K, 
0,  0,  0  and  L,  Fig.  8,  trace  the  contour  of  moulding  require«l 
for  the  cap.  The  pattern  maybe  made  similar  to  that  at  Fig.  7, 
Plate  4,  which  should  l)e  two  or  three  inches  long  for  hand  hold. 
If  this  pattern  be  neatly  made,  and  in  the  hands  of  a  good,  prac- 
tical turner,  the  cap  will  member  at  the  miter  with  the  connnon 
moulding. 


PLATE  7. 

The  Face-Mould. 

The  eicbt  following;  plates  are  intended  as  lessons  for  the  young  man 
to  draw  the  f  aco-iaould,  and  make  models  for  a  wreath-piece.  The 
triangular  sj^stcni  heroin  set  forth  is  believed  by  the  author  to  be  llie 
most  economical  method  for  tlie  construction  of  face-moulds  ovvv 
ground  plans  of  large  diameter,  or  over  winders.  The  half  size  of 
rail  will  suit  best,  for  the  models;  pine,  or  some  soft  wood,  may  be 
used  for  practice.     If  the  drawing  is  made  one-quarter  full  size,  theu 


Pr.ATE  7.  ?.7 

"soap  *  may  be  used,  wliioh  may  bo  cut  out  with  the  knife;  tins  last 
inethocl  will  do  for  studying  tlie  application  of  bevels,  and  the  sliding 
of  the  mould ;  but  does  not  iucreaso  the  skill  of  the  young  man  in  the 
useof  his  tools;  to  be  a  good  Staii-builder,  he  must  be  expert  in  work- 
ing witli  the  drawing-knife  and  spoke-shave,  in  which  there  is  a 
great  sleight. 

Plate  7.  [Scale,  1}.^^^=V.]  Exhibits  the  construction  of 
the  Face- inonhl  for  a  Wrcath-2iiece  of  a  Hand-rail,  to  stand  over 
a  quarter  circle  on  plan,  the  radius  for  the  center  li7ie  hcing 
Ih".  The  Wreath-piece  to  contain  a  full  casing,  hence  one  tan- 
gent irlll  be  inclining,  and  the  other  horizontal;  the  rail  to  be 
3^'  wide  by  4}4''  deep. 

As  the  wreatli-piece  is  to  contain  a  full  easing  over  a  ground 
plan  of  one-quarter  circle,  the  face-mould  will  be  one-quarter  of 
an  ellipse,  the  axis  of  which  will  form  the  joints  of  the  wreath- 
piece.  Also  one  bevel  only  will  be  required,  that  at  the  joint  on 
the  major  axis,  which  will  be  at  the  wide  end  of  mould;  the  square 
will  be  applied  at  the  joint  on  the  narrow  end  of  face-moidd, 
which  will  be  ou  the  minor  axis. 

Fig.     1.     Shows  the  g,  oimd  plan  of  the  Quarter  Circle. 

Draw  OA  and  OB  at  right  angles,  with  OA  [ir/^]  for  a 
radius,  draw  the  dotted  line  ASB  for  the  center  of  rail.  Make 
A  2,  A  3  each  epual  half  the  width  of  the  rail  [l.Vi'^].  Draw  the 
width  of  rail,  2  4  and  3  6,  for  the  cylindric  section  ou  plan.  Draw 
tlie  tangents  AD  and  BD  perpendicular  to  the  radial  lines  OA 
and  OB,  and  we  have  the  square  parallelogram  OABD  on  plan. 
Draw  the  chord  AB,  bisect  AB  at  C ;  bisect  CSand  CA  at  E 
and  F;  bisect  Ai^at  G  ;  in  this  case  the  tangent  AD  will  be  the 
director  of  ordinates,  because  the  wreath-piece  is  to  have  a  full 
easing.  Parallel  with  the  director  AD,  draw  ordinates  from  the 
points  GFC  and  E  to  intersect  the  concave,  convex,  and  center 
lines  at  the  points  2,  4  and  3. 

Fig.  2.  Shows  the  developynent  and  elevation  of  Tangents 
from  plan. 

Let  XX  indicate  a  base  line.  Make  HD  and  DA  e(jual  the 
tangents  BD  and  DA  on  plan.  Fig.  1 ;  draw  AE,  DF  and  HG, 
perpendicular  to  XX.  Assume  HB  to  be  the  height  the  wreath- 
piece  is  required  to  raise  ;  connect  BD,  for  the  length  of  tangent 
in  elevation,  that  will  stand  over  tangent  BD  on  plan.  Fig.  1;  the 
other  tangent,  AD,  is  horizontal  for  a  wreath-piece  having  a  full 
easing,  and  its  length  remains  the  same  as  ou  plan  [IS^^J. 

Make  ifj" equal  the  chord  AB,  on  plan.  Fig.  1,  parallel  with 
the  perpendicular  DF,  draw  the  half  width  of  rail,  cutting  the 
tangent  DB  at  2  ;  then  D  2  will  be  the  increased  width  for  half 
the  mould  at  the  wide  end. 

Bevel.  In  this  case  but  one  bevel  is  required,  and  that  is 
found  as  shown  in  the  angle  at  B. 

Fig.  3.    Exhibits  the  Face-mould. 

Draw  the  right  angle  BDA  indefinite  ;  make  DB  equal  tan- 
gent DB,  Fig.  2.  Let  DA  equal  tangent  DA  on  plan.  Fig.  1, 
Parallel  with  tangents  DB  and  DA,  draw  AO  and  BO,  and  we 
liave  the  rectilineal  parallelogram  OADB  on  the  eutting  plane, 
or  plane  of  plank,  that  will  stand  over  the  square  parallelogram 
OADB  on  plan.  Fig.  1. 

"  Proof.  The  chord  AB  and  diagonal  DO,  must  each  equal 
BJ,  Fig.  2.  Draw  the  chord  AB  ;  bisect  AB  at  C ;  bisect  BC 
and  CA  at  E  and  F ;  bisect  AF  at  G,      Now,  in  this  case,  the 

*Recommeuded  by  Mr.  Collins,  in  the  Eneycloxjcdla  of  Architecture. 


38  Plate  7. 

tangent  AD  becomes  the  director;  draw  ordiuates  from  th^ points 
G,  F,  Caiid  E,  indefinite,  and  parallel  to  the  director  AZ);  make 
A  4;  G,  2,  3,  4;  C,  2,  3,  4;  B  A\  B  G,  &c.,  each  equal  correspond- 
ing points  on  plan,  Fig.  1. 

Make  A  7  and  A  8  each  equal  D  2  in  elevation.  Fig.  2  ;  now 
trace  the  curves  for  the  center,  concave  and  convex  sides  of 
mould,  through  the  points  as  shown,  using  a  flexible  strip.  If  a 
trammel  or  rod  be  preferred,  O  is  the  center  for  the  trammel  and 
the  semi-minor  axis  OB  and  semi-major  axis  OA  are  given. 

For  long  face-moulds  the  use  of  ordinates  in  this  way  will  be 
found  more  convenient,  as  the  work  c:in  be  done  in  less  space,  and 
any  number  of  pouits  in  the  elliptic  curve  can  be  established  correct 
enough  for  practice. 

The  trammel,  bowever,  gives  the  elliptic  curve  for  face-moulds 
absolutely  correct,  for  all  wreatb-pieces,  standing  over  a  ground 
plan,  tliat  is  a  portion  of  u  true  circle. 

The  rod  may  lie  u^.ed  instead  of  a  trammel,  as  shown  at  Fig.  2, 
Plate  4. 

The  section  at  M  shows  the  bevel  applied  from  the  face  of 
crook,  through  the  center  of  plank ;  the  dotted  line  indicates  a 
gauge  line  determining  the  center  of  plank,  and  is  applied  the 
same  at  both  joints  so  as  to  have  the  wreath- piece  taken  from  the 
center  of  plank.  Now,  make  a  "Block  Pattern "  of  thin  stuff  to 
the  size  required  for  the  rail;  in  this  case,  3^''yi}^^^,  as  indicated 
at  M  aw\  N;  have  a  line,  2  3,  drawn  through  tlie  center,  and  a 
small  screw  filed  off  to  a  point  placed  in  the  center  O,  so  that  a 
light  tap  with  the  hammer  will  hold  the  pattern  in  place. 

The  pattern  is  centered  at  the  intersection  O,  made  by  the 
gauge  line,  and  the  tangent  AD,  that  is  squared  over  the  joint, 
through  which  the  bevel  found  in  the  angle  at  B,  Fig.  2,  is 
applied  ;  and  the  line  3  2,  on  the  block  pattern  is  made  to  agree 
with  the  bevel  line;  then  scribe  around  the  pattern  for  the  section 
of  rail  on  the  joint.  At  section  N  the  try  square  Is  applied 
through  the  center  of  crook,  from  the  face  of  plank  ;  the  block 
pattern  is  centered  at  the  intersection,  and  is  governed  by  the 
square ;  the  shaded  parts  show  the  amount  of  over  wood  that  has 
to  be  removed  in  the  formation  of  the  wreath-piece. 

Fig.  4.  Exldhits  an  isometrical  view  of  the  plan,  elevation 
and  center  line  of  Face-movhl.  on  the  cutting  plnne  OADH. 

The  plan  of  tangents  OABD  agrees  with  those  at  Fig.  1 ; 
JBif  is  the  height:  BA  the  chord  on  plan,  and  HA  the  chord  in 
elevation.  The  dotted  line  AJB  indicates  the  center  line  of  rail 
on  plan,  and  AJHXhQ  center  line  on  the  cutting  plane. 

The  chord  AB  on  plan,  is  bisected  at  the  points  E,  C,  F,  G, 
in  manner  as  described  at  Fig.  1 ;  the  ordinates,  3  G,  3  F,  Ac.  are 
made  parallel  to  AD.  From  the  points  E,  C,  F,  G,  perpendiculars 
are  drawn,  cutting  the  chord  HA  in  elevation,  and  dividing  HA 
proportionately  with  the  chord  BA,  on  plan.  Ordinates  are  again 
drawn  ;  this  time  from  the  chord  HA,  in  elevation,  parallel  with 
DA;  the  points  in  the  ordinates  on  the  horizontal  plane  are  trans- 
ferred to  corresponding  ordinates  on  the  cutting  plane,  using  tlie 
chords  AB  and  AH  as  a  base. 

The  curve  traced  through  the  points  H,  3,  3,  A,  shows  the 
center  line  of  rail  on  the  cutting  plane,  and  indicates  the  dotted 
line  on  the  center  of  face-mould,  Fig.  3.  The  student  will  see 
through  this  more  readily  by  the  study  of  blocks  or  prismatic 
solids ;  dress  up  a  block  five  or  six  inches  long,  say  2^'  square, 
cut  it  to  the  bevel  sliown  at  J5,  Fig.  2,  across  its  two  opposite  sides, 
the  other  two  sides  will  be  square  to  the  face ;  then  by  dividing  it 
across  the  angles,  as  ABHA  on  the  chord  lines,  into  two  triangu- 
lar prisms,  he  will  see  at  once  the  whole  system  in  a  "  uutsbell." 


Plate  7.  39 

Fig.  5.  Shows  the  manner  of  cutting  out  the  crook  from 
the  plank;  then  applying  the  bevels,  and  sliding  the  moulds. 

One  may  be  able  to  draw  a  correct  face-mould,  and  yet  fail  in 
applying  the  bevels  and  sliding  the  mould.  The  shaded  part  at 
sections  M  and  N,  Fig.  3,  show  the  width  at  the  joints  required 
for  the  wreath-piece  to  square  ;  at  iV,  98^^ on  the  concave  and  j^^^ 
on  the  convex  side,  is  enough  wood  to  allow.  In  this  case,  obsei've 
the  wide  end  of  mould  about  equals  the  width  of  shaded  section 
at  M,  but  at  N  the  section  is  a  little  wider  than  the  mould,  to 
allow  for  dressing  down.  Now  lay  the  pattern  on  the  plank, 
mark  the  convex  side,  then  shift  the  mould  at  the  narrow  end  to 
the  required  width  shown  by  the  section,  and  mark  the  concave 
side  of  mould  ;  also  at  the  joints  allow  K^'  for  jointing,  then  cut 
out  square  through  the  plank.  The  band  saw  is  the  best  tool  for 
this  work  ;  now  dress  off  the  upper  side  of  crook  true,  and  out  of 
wind,  this  must  be  carefully  done  for  the  face-mould,  and  bevels 
may  all  be  correctly  drawn,  and  if  the  crook  be  not  true  on  its 
face,  the  work  will  not  prove  satisfactory.  Now,  mark  the  tan- 
gents on  both  sides  of  the  face-mould,  directly  opposite  to  each 
other.  Do  this  on  all  face-moulds.  The  heavy  lines,  2  3,  4  5, 
show  the  joints  of  crook  for  the  wreath  piece ;  place  the  mould 
on  the  crook  keeping  it  in  the  center  of  the  stuff  on  its  face.  Now 
carefully  mark  the  joints  2  3  and  4  5,  and  also  mark  the  tangents 
shown  by  the  heavy  lines  AD  and  SD;  see  while  doing  this  the 
mould  does  not  shift ;  now  lift  the  pattern  and  complete  the  mark- 
ing of  the  tangents  on  the  face  of  crook,  then  square  and  cut  the 
joints  2  3  and  4  5,  dress  the  joints,  square  to  the  face  of  crook,  and 
also  square  to  the  tangents,  by  applying  the  stock  to  the  joint  and 
the  blade  along  the  tangent ;  then  carry  the  tangents  across  the 
joints,  square  to  the  face  of  crook  as  shown  by  the  heavj'  lines, 
through  the  center  of  sections  at  M  and  N;  then  mark  the  tan- 
gents AD  and  ED  on  the  other  side  directly  opposite  and  square 
to  the  joints.  Now  set  a  gauge  to  the  half  thickness  of  plank,  and 
center  the  crook  as  shown  by  the  dotted  lines  on  sections  JJf  and 
N;  then  at  M  apply  the  bevel  found  in  the  angle  at  B,  Fig.  2, 
from  the  face  of  crook,  through  the  intersection  made  by  the 
gauge  line. 

Next  apply  the  block  pattern  square  to  the  line  made  from 
the  bevel,  mark  around  the  same  for  the  section  of  rail ;  proceed 
in  the  same  manner  at  section  N,  using  the  try  square  instead  of 
a  bevel.  Now  let  it  be  observed  the  center  line  at  section  M, 
made  by  the  bevel,  intersects  the  face  of  crook  at  (S  ;  then  squr.re 
.icross  on  the  upper  side  of  crook  parallel  with  AD  the  line  6  D: 
on  the  under  side  of  crook,  the  point  7  extends  beyond  the  face  of 
crook  in  this  case,  and  the  tangent  cannot  be  marked  on  the  crook. 

At  section  iVthe  square  is  shown  applied,  and  the  tangent  C 
H,  on  the  face-mould  will  rest  over  the  tangent  BD,  on  the 
crook;  and  tlie  tangent  6  F  on  the  face-mould  will  rest  over  the 
tangent  6  i)  on  the  crook. 

The  light  solid  lines  h,  10,  and  9,  16.  11,  show  the  face-mould 
applied  to  the  face  of  crook.  Observe  it  is  shifted  from  A  to  6  at 
the  lower  end,  and  the  same  distance  from  B  to  C,  at  the  upper 
end,  on  the  upper  side  of  crook  ;  and  on  the  under  side  of  crook, 
the  dotted  lines  12,  13, 14  and  16,  D  15,  show  tho  face-mould  has 
shifted  from  JB  to  .E7  at  the  upper  end,  and  from  A  to  7  at  the 
lower  end.  As  wc  cannot  mark  the  tangent  on  the  crook  at  7,  on 
the  under  side,  slide  the  mould  on  the  crook  until  the  center  line 
made  by  the  bevel  shown  at  section  Jf,  Fig  6,  will  line  with  the 
tangent  on  the  mould  shown  at  7,  keeping  the  joint  ou  mould  even 
•with  the  joint  on  crook ,  and  also  the  tangent  on  the  mould  at  the 


40  Plate  7. 

narrow  end  must  lie  over  the  tangent  BD,  on  the  crook.  Observe 
now  the  face-monld  on  the  upper  side  of  croolc  lias  shifted  from 
B  to  C,  at  the  narrow  end,  while  the  mould  shown  by  the  dotted 
line  has  shifted  from  J5  to  jE7  on  the  lower  side.  Note  also  the 
joint  at  the  wide  end  of  mould  is  on  line  with  the  joint  of  crook; 
the  joint  therefore  answers  for  a  slide  line  when  sliding  the 
mould,  this  is  always  the  case  when  the  plank  is  canted  only  one 
way,  as  in  this  case.  Now  scribe  around  the  mould  ou  the  upper 
side  of  crook,  on  the  convex  side,  8  FH  10,  and  also  for  a  short 
distance  at  5,  ou  the  concave  side,  the  balance  of  mould  leaves  the 
crook. 

On  the  under  side,  scribe  around  the  mould  on  the  concave 
side  12,  13  and  14,  and  for  a  short  distance  at  1.5,  on  the  convex 
side,  the  balance  of  mould  on  the  convex  side  leaves  the  crook. 
Observe  the  scribe  lines  at  14  and  1.5,  do  not  extend  to  the  joint 
4  .5  ;  they  may  be  carried  to  the  joint  leading  a  small  amount  on 
eacli  side  of  the  block  pattern  to  be  dressed  off  when  the  adjoining 
wreath  piece  is  connected.  Also  note  the  curve  of  face  mould  on 
tlie  upper  side  of  crook,  at  joint  B,  cuts  the  joint  to  one  side  of 
the  block  pattern  as  shown  by  the  dotted  lines  at  a  and  b.  Do 
not  be  alarmed  at  this  seeming  disagreement,  for  the  ))lock  pattern 
does  not  give  the  correct  contour  or  outline  of  the  squared  section 
of  rail  for  a  joint  within  the  wreath,  when  the  plaue  of  joint  is 
oblique  to  the  axis  of  cylinder,  as  at  joint  B,  it  being  at  right 
angles  to  the  inclination  of  tangent  BD.  For  this  reason  all 
wreaths  that  have  their  joints  obliciue  to  the  axis  of  cylinder 
should  be  worked  off  to  the  bevels,  leaving  some  over  wood  at  the 
joints  to  be  taken  off  when  they  are  bolted  tog<,'ther.  When  the 
wreaths  are  separated  it  will  be  seen  that  tiie  sides  of  the  section 
are  concave  on  the  concave  side,  and  convex  on  the  convex  side  of 
rail ;  this  curve  is  elliptical  and  tangents  the  block  pattern  at  the 
center  of  rail,  as  sliown  by  the  dotted  lines  at  section  N,  Fig,  6. 

The  joint  at  A  is  different,  it  being  a  plumb  joint,  the  tan- 
gent AD  being  level,  conseciueutly  the  joint  wiil  be  parallel  to  the 
axis  of  cylinder,  and  the  block  pattern  gives  the  true  contour  of 
the  squared  section  of  rail. 

All  joints  that  are  made  s(|uare  to  inclining  tangents  are 
oblique  to  the  axis  of  cylinder.  If  the  joint  at  B  was  joined  to 
straight  rail,  then  the  contour  of  the  squared  section  of  rail  would 
be  curved  at  the  upper  side  down  to  the  center  of  joitit.  and 
straight  from  that  to  the  lower  side,  the  curve  forming  a  tangent 
to  the  side  of  block  pattern  at  the  center  of  rail.  The  straight 
jiart  belongs  to  the  straight  part  of  rail  and  terminates  at  the 
spring  of  cylinder,  as  shown  by  the  dotted  line  JK,  Fig.  0.  The 
triangular  piece  at  J"  shows  the  straight  i)art.  Suppose  the  joint 
at  B  to  be  plumb,  or  a  splice  joint  on  the  line  JK,  Fig.  G,  instead 
of  a  butt  joint,  then  it  will  be  seen  that  the  two  sides  of  the 
squared  section  of  lail  would  be  straight  and  parallel  to  each 
other,  and  the  plane  of  the  joint  would  be  parallel  to  tlie  axis  of 
the  cylinder;  then  the  wreath  piece  would  cover  exactly  one- 
quarter  of  the  circle.  This  being  a  butt  joint,  it  will  be  observed 
the  triangular  ))iece  between  if  and  .B,  Fig.  6,  is  cut  away,  and 
must  be  supplied  by  the  adjoining  wreath -piece,  which  makes  up 
for  the  seeming  disagreement  at  4  and  5,  Fig.  5.  In  the  same  way 
the  triangular  piece  at  J  makes  up  for  the  lower  side  of  the  ad- 
joining wreath-piece. 

For  this  reason,  a  joint  connecting  a  wreath-piece  with  tlie 
straight  rail  should  never  be  made  at  the  spring  line,  but  add  on 
some  straight  wood,  at  least  what  the  mould  would  slide,  as  BC, 
Fig.  5.    For  wreaths  on  winders  conuectiug  ramps,  the  distance 


Plate  8.  41 

BC  or  A  6,  Fiff.  5,  will  be  enough  straight  wood  to  add  for  shank; 
but  for  wreath-pieces  on  platforms,  or  level  landings,  &''  straight 
wood  for  shanks  is  a  fair  allowance,  to  ease  off  the  straight  rail, 
into  the  wreath  part  ;  and  should  be  measured  in  and  priced  as 
wreath  rail,  as  the  labor  on  this  part  of  wreath- piece  is  equal  to 
that  of  any  other  part. 

Fig.  6.  Shoics  the  concave  Ride  of  crook  turned  up,  having 
the  concave  side  worked  off  to  the  bevel  and  square,  and  the  face- 
mould  (S>S  shifted  on  the  upper  and  lower  side  so  that  the  center 
of  mould  agrees  with  the  center  line  6  7,  made  from  the  bevel 
through  the  center  of  crook. 

Two  face-moulds  are  shown  here  but  only  one  is  required ;  it 
will  be  observed  that  by  tacking  the  face-mould  on  the  upper  side 
of  crook,  the  edge  9,  16,  11  Fig.  5,  will  serve  for  a  guide  to  work 
off  the  concave  side  of  wreath-piece  to  the  required  bevel. 

The  scribe  line  12,  13,  14,  Fig.  5,  on  the  opposite  side  of 
crook  serves  as  a  guide  to  shape  the  wreath  piece  for  the  lower 
side.  For  the  convex  side  of  wreath  piece,  if  the  face-mould  be 
tacked  on  to  the  lower  side  of  crook,  the  edge  of  pattern  will  give 
the  line  for  the  convex  side  of  wreath  piece  ;  the  scribe  line  8,  F. 
H,  Fig.  5,  gives  the  curve  of  mould  on  the  upper  side  of  crook. 

The  surplus  wood  should  be  removed  from  the  concave  side 
first,  then  the  best  way  is  to  gauge  for  the  convex  side,  using  the 
"Cupper  gauge,"  shown  at  Figs.  13  and  14,  Plate  21.  After  the 
wreath  piece  is  shaped  to  the  bevel  on  the  concave  and  convex 
sides,  then  use  a  pliable  strip  to  form  the  twist  of  wreath  as  shown 
at  2,  3,  B.  Falling-moulds,  made  of  paste  board  or  tin,  to  the 
required  depth  of  rail,  were  made  in  former  days,  to  obtain  the 
falling  line  of  the  wreath  piece;  now  a  thin  strip  }4''^  wide  and 
one-sixteenth  thick,  is  bent  around  the  convex  and  also  on  the 
concave  side  of  wreath  piece  and  the  twist  line  traced  agreeably 
to  the  eje,  the  thin  strip  is  easily  adjusted  so  as  to  avoid  any 
kinks  or  abrupt  places.  Next  take  oft"  the  surplus  wood  from  the 
top  side  of  wreath  piece  first ;  when  dressed  oft',  to  please  the  eye 
and  touch;  gauge  for  the  lower  side. 

Kemember  when  dressing  off  the  wreath  piece  use  the  tools 
so  as  to  conform  to  the  pilch  of  wreath  piece  as  JK,  Fig.  6  ;  this 
direction  is  very  easy  found  at  any  time  by  marking  the  end  of 
mould  on  the  crook,  as  15,  14,  Fig.  5  ;  then  a  line  from  14,  through 
5,  Fig.  G,  gives  the  direction  for  the  tool ;  pencil  lines  parallel  to 
5  14,  may  be  drawn  with  a  parallel  ruler  from  end  to  end  of  the 
wreath  piece  as  a  guide  for  the  tools.  A  large  gouge  and  mallet 
are  about  the  best  tools  to  rough  down  the  surplus  wood,  then  use  the 
drawing-knife,  cylinder-plane  and  spoke-shave  to  dress  off  to  the 
concave  arris  of  the  face-mould ;  also  use  a  short  straight-edge  to 
rest  on  the  arris  of  mould  and  the  scribe  line  on  tlie  crook,  in  the 
direction  of  JK,  Fig.  6,  as  a  guide  to  true  up  the  concave  side  of 
wreath  piece. 


PLATE    8. 


Plate  8.  E.rhihilfi  how  to  draw  the  face-mould  for  a 
quarter  circle  for  a  wrauli-picce  having  an  intermediate  easing ; 
Vie  tangents  ivill  he  diffe/cnLin  their  inclination,  hence  two  bevels 
■will  he  required. 

Pig.  1.  Shows  the  plan  of  the  quarter  circle.  Draw  OA 
and  OB  indefinite,  and  at  right  angles.  From  the  center  O 
diaw  the  quarter  circle  ASB  to  the  radius  of  15'^ ;  draw  the  tau- 


43  Platr  8. 

gents  A^  and  BD  square  to  the  radial  lines  OB  and  OA;  on 
each  side  of  A,  set  ofiE  the  half  width  of  rail  [13.^  ^']  as  A  2  and  A  4; 
from  the  center  O  draw  the  concave  side  of  rail  2,  3,  2,  and  also 
the  convex  side  4,  4,  4,  thus  completing  the  cylindric  section  3,  3, 
3,  and  4,  4,  4,  on  plan.  Draw  the  chord  AB;  bisect  the  chord  at 
C;  bisect  CB  and  CA  at  ^aud  F;  bisect  AJF*  at  Gr, 

Fig.  2.  Exhibits  the  dei^elopment  and  elevation  of  tangents 
from  the  plan,  Fig.  1.  Let  XX  indicate  a  base  line.  Make  B£> 
and  DA,  equal  the  tangents  BD  and  DA  on  plan  Fig.  1;  perpen- 
dicular to  XX,  draw  BC,  DE  and  AF.  Assume  BC  to  be  the 
height  the  wreath  piece  has  to  raise;  from  C  and  square  to  CB, 
draw  CE  prolonged.  Also  assume  the  inclination  of  the  lower 
tangent  to  cut  DE  at  G.  draw  CG  prolonged  to  intersect  XX  at 
H,  draw  the  tangent  AG  to  intersect  BC  at  J.  From  D,  and 
square  to  CH,  draw  Dk;  from  E,  and  perpendicular  to  AJ, 
draw  J57I/.  Make  CM  eciual  the  chord  AJ5  on  plan,  Fig,  1. 
Parallel  with  DE.  draw  the  half  width  of  rail,  cutting  the  tan- 
gents AG  and  CG  at  3  and  3  respectively. 

Bevels.  Let  PiV  indicate  a  line  dravra  parallel  with  XX: 
draw  PQ  square  to  XX,  and  equal  to  the  radius  OA,  Fig.  1. 
Make  PSequ-alDK,  and  Pieequal^I,;  draw  QR  and  QS,  and 
in  the  angle  PSQ,  is  found  the  bevel  for  the  joint  of  wreath- 
piece  at  the  narrow  end  of  face-mould,  and  in  the  angle  PRQ  is 
found  the  bevel  for  the  joint  at  the  wide  end  of  mould.* 

Fig.  3.  Exhibits  the  face-mould.  Make  the  tangent  BD 
equal  CG,  Fig,  3  ;  with  S  as  a  center,  and  MB,  Fig.  3,  for  a 
radius,  draw  arc  at  A;  again,  with  D  as  a  center,  and  GA,  Fig. 
2,  for  a  radius,  draw  arc  intersecting  at  A,  connect  DA;  parallel 
with  DA  and  DB,  draw  BO  and  AO,  for  the  parallelogram 
AODB,  on  the  cutting  plane,  that  will  agree  when  in  position, 
with  the  square  parallelogram  OADB  on  plan  Fig.  1. 

Proof.  The  diagonal  OD  must  equal  the  distance  MJ,  Fig. 
3 ;  if  so,  the  parallelogram  is  correct.  Make  BH  equal  GH, 
Fig.  3  ;  draw  HO  for  the  direction  of  minor  axis  ;  make  A  2  and 
A  4  each  equal  G  3,  Fig.  3;  make  B  3  and  B  4  each  equal  G  2, 
Fig.  2,  draw  the  chord  AB;  bisect  AB  at  C;  bisect  CA  and  CB 
at  F  and  E;  bisect  AF  at  G;  from  the  points  A,  Gr,  F,  C,  B 
and  B  draw  ordinates  indefinite  and  parallel  with  the  director 
HO.  On  plan.  Fig.  1,  make  BIT  equal  DH,  Fig.  2,  join  HO  for 
the  directing  ordinate;  from  the  points  A,  G,  F,  C,  E  and  B 
draw  ordinates  parallel  to  HO,  cutting  the  concave,  center  and 
convex  sides  of  rail  in  the  points  2,  3,  4.  Now  transfer  the  points 
in  the  ordinates  Fig.  1,  to  the  corresponding  ordinates  Fig.  3, 
using  the  chords  as  base  lines,  then  trace  the  curves  through  the 
points. 

Make  the  joints  at  A  and  B  square  to  the  tangents  AD  and 
BD.  The  sections  at  M,  show  the  joint  centered  by  the  dotted 
line,  and  the  tangent  line  is  squared  over  the  joint  intersecting  the 
gauge  line  ;  the  bevel  at  R,  Fig.  2,  is  applied  through  the  inter- 
section, from  the  face  of  crook. 

♦When  the  tangent.s  happen  to  be  nearly  the  same  length,  the 
difference  in  width  of  the  face-mould  at  the  jbint.swillbe slight;  then 
apply  tho  steepest  hevel  to  the  joint  tliat  has  the  radial  line  the 
greatest  distance  from  the  minor  axis.  In  that  case  the  minor  axis 
should  always  he  drawn  on  tlie  mould  whenever  practicable.  Another 
sure  way  is  to  apply  the  steepest  bevel  to  the  joint  that  is  made  from 
the  shortest  tangent ;  this  rule  applies  to  all  face-moulds  for  wreath 
pieces  that  are  circular  on  plan. 


Plate  8.  43 

Observe  the  bevel  as  applied,  will  raise  the  joint  at  B  up. 
The  section  at  iV"shows  the  tangent  squared  across  the  joint,  and 
the  same  gauge  as  applied  at  M  gives  the  intersection  through 
which  the  bevel  found  in  the  angle  at  S,  Fig.  2,  is  applied.  Ob- 
serve the  bevel  is  applied  the  opposite  from  that  at  M,  and  will 
cross  *  the  tangents,  and  thus  pitch  the  joint  at  A  down.  The 
shaded  parts  at  ilf  and  iVshow  the  width  to  saw  out  the  crook  at 
the  joints.  To  find  the  amount  of  over  wood  required  at  Kon  the 
normal  line  GK,  to  saw  out  the  crook ;  take  F,  Fig.  1,  as  a  center 
and  FC,  Fig.  3,  for  a  radius  ;  draw  arc  cutting  the  diagonal  OD 
at/,  join  fF;  draw  the  half  depth  of  rail,  [2^^^]  parallel  with 
Ff,  cutting  DO  at  b;  from  b  and  square  to  Ff,  draw  bJ.  From 
J"  draw  a  line  parallel  to  OD,  cutting  the  concave  curve  of  rail  at 
h;  from  h  and  at  right  angles  to  OD,  draw  he;  then  from  c  to 
the  concave  curve  is  the  amount  of  over  wood  required  on  the 
concave  side  of  mould  at  the  normal  line  or  point  K,  Fig.  3.  On 
tlie  convex  side  only  enough  over  wood  to  clean  off  the  saw  marks, 
say  J^'^,  is  all  that  is  required,  but  the  amount  increases  grad- 
ually towards  the  ends,  to  the  amount  shown  by  the  shaded  parts, 
at  sections  M  and  N. 

Fig.  4.  Exhibits  an  isometHcal  vie^v  of  the  ground  plan, 
elevation,  governing  ordinate,  and  the  center  line  of  rail  on  the 
cutting  plane.  It  is  not  intended  for  a  working  drawing,  but 
simply  to  show  from  the  triangular  prisms  the  construction  of 
lines,  to  find  the  cutting  plane  and  the  direction  of  the  governing 
ordinate  on  the  horizontal  and  cutting  planes. 

The  learner  will  find  it  a  great  advantage  to  cut  blocks  to  the 
inclination  of  tangents,  whfiu  drawing  his  face-moulds,  and  from 
them  he  will  discern  more  clearly  the  reason  for  this  or  that  line. 
This  is  termed  Stereotomy,  or  the  study  of  the  Science  of  Solids. 
The  stone  cutters  are  noted  for  tliis  study,  as  one  expert  in  the 
business  can  tell  at  once  if  what  he  requires  is  in  a  particular 
solid. 

OABD  shows  the  ground  plan  as  described  at  Fig.  1,  and 
indicates  the  end  of  two  triangular  blocks  forming  a  square  and  is 
supposed  to  be  a  horizontal  plane  :  ASB  shows  the  center  line  of 
rail  on  plan;  AB,  the  chord  ;  DG,  on  edge  of  solid  equals,  the 
height  DG,  Fig.  2;  00,  on  the  opposite  corner  of  solid  equals  G 
E,  Fig.  2;  SP  indicates  another  corner  of  the  solid,  and  equals 
the  whole  height  as  shown  at  BC,  Fig.  2;  draw  AO,  and 
AG,  connect  PG  and  AO,  also  PO  for  the  parallelogram 
AGPO  on  the  cutting  plane,  which  indicates  the  parallelo- 
gram for  the  face-mould.  Fig.  3.  Now  to  find  the  directing 
ordinate  on  the  horizontal  plane,  prolong  BD  indefinite, 
prolong  PG  to  intersect  BD  prolonged,  at  Q,  join  QA,  for 
the  director  sought;  this  line  is  termed  the  "intersecting  line," 
by  some;  the  "level  "  or  "  horizontal  line,"  by  others;  the  direc- 
tion of  the  minor  axis  is  always  parallel  with  this  line.  If  the 
other  side  SO  of  solid  were  prolonged  same  as  BD,  and  PO,  also 
prolonged  to  intersect  BO,  then  if  a  line  be  drawn  from  the  inter- 

*The  term  "cross"  or  "crossing  the  tangents,"  means  that  the 
bevels  are  applied  to  the  opposite  sides  of  tangents  at  the  joints.  Ob- 
serve at  joint  A,  section  M,  tlie  bevel  points  to  the  right  of  the  tan- 
gent AD.  Let  the  eye  follow  the  tangents  around  to  joint  B,  and  the 
sharp  angle  of  bevel  is  seen  to  point  to  the  opposite  side  of  tangents 
at  section  N,  thus  crossing  the  tangents.  This  will  be  the  case  with 
all  wreath  pieces  having  two  bevels,  when  the  curve  on  plan  is  a 
Quarter  circle  or  more  than  a  quarter  circle  ;  it  is  only  when  the  plan 
is  less  than  a  quarter  circle  that  the  bevels  do  not  cross  ;  and  then 
only  when  the  minor  axis  is  not  in  the  mould. 


44  Pl.ATE   8. 

section  to  the  point  Q,  the  line  would  pass  through  the  point  A, 
thus  showing  the  line  QA  to  result  from  the  intersection  of  the 
two  inclinations  with  the  horizontal  plane.  If  the  learner  would 
dowel  on  the  triangular  prisms  DQAG  to  the  side  of  the  solid  D 
GA,  and  do  the  same  at  the  adjoining  side  AOO,  then  cut  them 
to  the  inclination  of  the  cutting  plane,  he  will  then  see  that  all  lines 
drawn  parallel  to  the  director  QA,  both  on  the  horizontal  and  cut- 
ting plane,  are  of  the  same  length,  those  on  the  cutting  plane 
being  parallel  to  those  on  the  horizontal  plane  and  all  parallel  to 
the  director  QA.  This  makes  a  fine  study  for  the  student  in 
stair-building. 

Make  JBH  on  the  horizontal  plane  equal  DQ;  join  HO  for 
the  director  within  the  parallelogram  OADB,  on  the  horizontal 
plane.  For  the  director  on  the  cutting  plane  AGPO,  make  iV 
equal  GQ,  join  JO  for  the  director  on  the  cutting  plane.  It  will 
be  observed  that  the  director  HO  on  the  horizontal  plane,  and  also 
the  director  JO  on  the  cutting  plane,  are  both  the  same  length, 
and  parallel  with  the  director  QA.  By  drawing  them  within  the 
parallelogram  it  saves  room  on  the  drawing  board ;  QD  is  repre- 
sented in  the  elevation  by  DH;  and  QG  by  HG,  in  elevation 
Fig.  2.  The  director  JO  on  tlae  cutting  plane  is  the  direction  of 
the  minor  axis.  If  a  line  through  O  be  drawn  at  right  angles  to 
JO,  it  would  be  the  direction  of  the  major  axis;  OiC  equals  the 
radius  OA,  Fig.  1,  for  the  center  line  of  rail,  and  is  the  semi-minor 
axis  of  the  elliptic  curve,  for  the  center  line  of  rail. 

AJB  is  the  chord  line  on  the  horizontal  i)lane ;  AP  is  the 
chord  line  on  the  cutting  plane,  and  represents  BM,  Fig,  2 ; 
the  chord  on  the  horizontal  plane  is  fust  spaced  off  then  the 
cliord  on  tlie  cutting  plane  is  divided  off  proportionately  with  the 
chord  on  plan,  as  shown  by  the  perpendicular  lines  CC,  EE,  &c. 

For  large  face-moulds  less  room  is  required  and  time  saved 
in  their  construction  by  the  use  of  ordinates  in  this  way,  as  shown 
in  the  triangular  prism  ABD  on  plan,  and  AFG  on  the  cutting 
plane.  Bisect  the  chord  AB  on  plan  at  C;  bisect  CB  and  CA 
at  E  and  F,  draw  F  3,  C  3  and  E  3  parallel  with  the  director  O 
H;  from  F,  C  and  E,  on  the  chord  AB,  erect  perpendiculars  to 
intersect  the  chord  AF  at  FC  and  E  on  the  cutting  plane  ;  thus 
dividing  the  chord  AP  in  elevation  proportionately  with  the 
chord  AB  on  plan.  From  the  points  F,  C  and  E  on  the  chord 
AP,  draw  ordinates  parallel  with  the  director  OJ;  then  transfer 
the  points  F3,  C  3,  from  the  ordinates  on  the  horizontal  plane  to 
the  coiTesponding  ordinates  on  the  cutting  plane,  and  trace  the 
elliptic  curve  through  the  points  A  3,  3  P,  using  a  pliable  strip. 

The  bevel  shown  at  the  angle  G  is  taken  from  the  angle  AG 
D,  Fig.  2,  and  the  bevel  shown  at  O  is  taken  from  the  angle  GC 
B  Fig.  2.  The  student  can  test  the  correctness  of  joint  bevels 
l>efore  applying  them  to  the  crooks  by  squaring  up  a  piece  2'^x 
2'^x6^''  long,  and  cutting  the  same  to  tlie  inclination  that  the  tan- 
gents in  elevation  make  with  the  pei"pendiculars  as  shown  ;  then 
by  applying  the  bevels  at  M  and  N,  square  to  the  inclination,  will 
pro\'e  their  correctness  ;  this  iloes  not  require  much  time,  and  will 
be  a  satisfaction  to  the  beginner  to  know  he  is  right  as  he  pro- 
ceeds with  his  work. 

Pig.  5.  Sliows  the  manner  of  sliding  the  mould.  The 
heavy  cur\  ed  line  indicates  the  crook  as  sawed  out  from  the  plank, 
llie  dotted  lines  at  the  ends  show  K^^  over  wood  to  make  the 
joints.  The  face  of  crook  must  be  carefully  taken  out  of  wind  ; 
then  place  the  face-mould  in  the  center  of  crook,  mark  the  joints, 
also  transfer  the  tangents    from    the    face-mould  to  the   crook ; 


Plate  8.  45 

also  mark  the  normal  line  LP.  Now  lift  the  mould  and 
finish  the  marking  of  tangents  AD  and  BD,  and  the  normal 
line  LP  on  the  face  of  crook.  Cut  and  dress  the  joints  square  to 
the  face,  and  also  S(iuare  to  tlie  tangents  ;  now  carry  the  tangents 
across  the  joints  square  to  tlie  face  of  crook  as  sho\Yn  by  the  heavy 
lines  S  3,  at  sections  M  and  N.  Then  turn  the  crook  over  and 
mark  the  tangents  on  the  opjiosite  side  squai'e  to  the  joints. 

Novvf  set  a  gauge  to  tlie  half  thickness  of  crook  and  mark  both 
joints  alike,  as  shown  by  the  dotted  line  00,  drawn  parallel  witli 
the  face  of  crook.  The  bevels  are  shown  applied  at  sections  M 
and  N,  through  the  intersection  made  by  the  gauge  line.  The 
block  pattern  is  then  applied  at  right  angles  to  the  center  line  G  7, 
made  from  the  bevels.  Observe  the  bevels  nie  applied  so  as  to 
cross  the  tangents,  and  also  that  they  cut  the  iip])er  side  at  6,  and 
the  lower  side  of  crook  at  7.  Now  A  4  and  B  4,  on  the  ui)per  side 
of  crook,  equals  2  6,  at  sections  Mand  N;  and  A  5  and  B  5,  on 
the  lower  side  of  crook,  eipials  7  3,  at  sections  M  and  N. 

From  4  and  5,  draw  4  D  and  5  D  parallel  to  tangents  AD  aiul 
BD;  this  should  be  carefully  done  as  these  lines  4  D  and  .5  D  are 
to  guide  the  face-mould.  Now  apply  the  face-mould  so  that  the 
tangents  8  D  and  9  D  on  the  mould  will  agree  with  the  tangent  4 
D  on  the  upper  side  of  crook.  Two  holes  are  seen  in  the  mould 
to  aid  in  arranging  the  mould  over  the  tangents  on  the  cr«X)k 
correctly.  If  the  mould  be  exact  over  the  tangents,  then  the 
joints  on  the  mould  will  be  parallel  with  the  joints  on  the  crook. 

When  the  tangents  on  the  mould  agree  with  the  tangents  on 
the  crook,  scribe  around  that  portion  of  the  mould  that  rests  ou 
the  crook,  then  transfer  the  minor  axis  G^iiC  from  the  mould  to  the 
crook  on  the  iipper  side.  Now  apply  the  moidd  to  the  opposite 
side  of  crook,  sliding  the  same  until  the  tangents  1:2  D  aiul  10  G 
on  the  mould  agree  with  the  tangent  5  D  on  the  crook,  then  scribe 
around  the  pattern  and  mark  the  minor  axis  as  before. 

At  H\\\Q  thickness  of  crook  is  turned  up  showing  the  i)attern 
applied  to  both  sides,  and  the  point -ffiT gives  the  direction  to  hold 
the  tools  when  removing  the  surplus  wood  from  tlie  concave 
side  of  the  wreath  piece ;  th(!  sections  M  and  N  show  the 
over  wood  removed  from  the  concave  side  and  ready  to  gauge  for 
the  convex  side,  or  if  preferred,  tack  the  mould  on  the  crook  and 
use  the  arris  of  the  mould  for  a  guide  where  the  scribe  line  runs 
out,  and  work  off  the  surplus  wood  to  the  distance  the  mould  will 
allow,  then  shift  the  mould  to  the  opposite  side  and  treat  in  the 
same  manner  at  the  opposite  end  of  crook. 

At  the  minor  axis,  and  for  some  distance  beyond  on  either 
side,  the  mould  will  be  in  the  way  and  must  be  removed,  then 
work  to  the  scribe  line  and  use  the  judgment  as  to  how  much  or 
little  to  take  off.  After  the  learner  has  S(inared  up  a  few  twists 
he  will  not  need  to  lack  on  the  face-mould  for  a  guide.  The  more 
practical  man  will  not  be  troubled  in  this  way,  but  proceed  at  once 
to  take  off  t!ie  surplus  wood,  guided  by  the  scribe  line  on  the 
crook  together  with  the  eye  and  judgment,  and  in  this  way  detect 
any  abrupt  places  in  the  curve.  Then  by  elevating  the  crook  into  its 
natural  position  by  standing  one  end  on  the  floor  while  the  other 
is  lifted  until  the  bevels  will  appear  plumb,  and  by  sighting  down 
and  around  the  curves,  he  will  detect  any  abruptness.  After  the 
sides  of  wreath  piece  have  been  formed,  then  bend  a  thin  strip 
around  the  concave  and  also  on  the  convex  side  of  large  twists, 
and  mark  the  twist  lines  of  the  wreath  piece,  keeping  the  section 
of  rail  at  the  minor  axis  LP,  in  the  center  of  crook,  for  here  at 
the  minor  axis,  the  bevels  l)lend,  and  the  section  of  rail  as  shown 
by  the  block  pattern,  is  at  right  angles  or  square  to  the  face  of 


46  Plate  9. 

crook  :  and  the  center  of  rail  is  in  the  center  of  crook,  as  shown  at 
Q;  QS  and  QT  being  equal  to  the  depth  of  rail  m"]. 

Dbserve  the  curved  sides  of  wreath  piece  as  shown  by  the 
dotted  lines  at  sections  Jlfand  JV,  tangent  the  block  pattern  at  the 
center.  This  is  mentioned  merely  to  warn  the  learner  not  to 
work  down  close  to  the  block  pattern  at  the  joints,  when  the 
joints  are  made  in  the  circular  part  of  wreath  piece,  but  leave 
some  wood  so  that  when  the  adjoining  wreath  piece  is  bolted  on, 
they  both  can  be  dressed  off  together,  holding  the  tools  perpen- 
dicular to  the  ground  plan.  If  straight  wood  be  added  on  at 
either  or  both  joints,  let  it  be  not  less  than  what  the  mould  slides, 
4  9  or  5  12  ;  then  the  block  pattern  will  give  the  true  contour  of 
rail  section. 

Comparing  Fig.  5  with  Fig.  .5,  plate  7,  it  will  be  observed  that 
the  face-mould  has  shifted  past  the  joints  A  and  B  at  both  ends, 
wliile  that  at  Fig.  5,  Plate  7,  the  joint  at  A  shows  the  pattern  has 
shifted  on  the  line  of  joint.  Tlie  reason  of  this  is,  because  in  the 
former  case,  both  tangents  in  elevation  Fig,  3,  are  shown  inclin- 
ing, and  the  mould  is  shifted  in  two  directions,  while  in  the  latter 
case,  one  tangent  is  inclining  and  the  other  is  level,  and  the 
mould  is  shifted  in  one  direction. 


PLATE    9. 


Plate  9.  [Scale  114^^='^  foot].  Exhibits  the  construction 
of  the  face-mould  for  a  wreath  jneee  over  a  quarter  circle, 
v^hen  tlie  tantjents  are  both  the  same  inclinatu>n.  Hence  Vie 
vjrcath  piece  u-ui  have  no  easinq,  aud  only  one  bevel  will  be 
required  for  both  joints  ;  the  width  of  rail  equals  3"  by  4)4'^ 
deep. 

Fig.  1.  Slutus  the  plan.  Draw  OA  and  OB  at  right 
angles  and  of  indefinite  lengtli.  Make  OA  equal  the  radius 
for  the  center  line  of  rail.  From  the  center  O,  draw  the  center 
line  of  rail  ASB,  make  A  2  and  A  3  each  equal  the  half  width 
of  rail ;  draw  the  concave  and  convex  sides  of  rail  2  7'2  and  3  H 
o.  Perpendicular  to  the  radial  lines  OA  and  OB,  draw  the  tan- 
gents AC  and  BC;  draw  the  diagonal  line  OC. 

Observe  when  the  tangents  on  plan  are  of  equal  lengtii,  and 
both  the  .same  inclination  in  elevation,  the  diagonal  OC  always 
becomes  the  director.  This  face-mould  is  very  simple  to  draw 
and  could  be  laid  off  on  the  plan,  to  avoid  a  net  work  of  lines, 
make  a  separate  drawing  for  the  face-mould. 

Draw  the  chord  AB,  bisect  the  same  at  D;  bisect  AD  aud 
DB  at  B  and  F;  bisect  AB  and  FB  at  G  and  H.  From  the 
points  A,  G,  E,  D,  F,  iif  and  JB,  draw  ordinates  parallel  to  the 
director  OC,  cutting  the  concave,  center  and  convex  sides  of  rail, 
at  2,  3  and  4. 

Fig.  2.  Exhibits  the  development  and  elevation  of  tan- 
gents. Let  XX  iudicate  the  edge  of  drawing  board  ,-  makeJSC 
and  CA  equal  the  tangents  BC  and  CA  on  plan.  Fig.  1.  At 
right  angles  to  XX  draw  the  perfjendiculars  AD,  CE  and  BF; 
assume  BG  to  be  the  height  that  the]  wreatli  piece  is  required  to 
raise.  Connect  AG,  cutting  the  perpendicular  CE  at  H.  From 
C  and  square  to  AH,  draw  Cj;  make  Sir  equal  the  chord  BA, 
iMir.  1 ;  parallel  with  CH,  draw  the  half  width  of  rail,  cutting  A 
H  at  2. 


Plate  9.  47 

Bevels.  In  this  case  both  tangents  liave  the  same  inclina- 
tion. As  a  result  only  one  bevel  will  be  required  for  both  joints. 
The  dotted  line  LM  indicates  a  gauge  line  parallel  with  XX. 
Make  MP  equal  CJ.  draw  MN  at  right  angles  to  XX,  and  equal 
to  the  radius  OB,  Fig.  1  ;  draw  NP  produced  to  the  edge  of 
board  for  convenience  when  adjusting  the  bevel,  as  sho^^'n.. 

Fig.  3.  Exhibits  the  facemonld.  Draw  AC  equal  to  the 
tangent  AH  in  elevation  ;  with  A  for  a  center,  and  KG,  in  ele- 
vation, for  a  radius,  draw  arc  at  G;  again  with  C  for  a  center, 
and  CA  as  a  radius,  draw  arcs  intersecting  at  G,  connect  CG. 
Parallel  with  CA  and  CG.  draw  GO  and  AO  for  the  parallelo- 
gram OACG,  on  the  cutting  plane ;  draw  the  diagonal  OC  tor 
the  director. 

Proof.  The  diagonal  OC  nnist  equal  the  diagonal  OC  on 
plan  Fig.  1 ;  if  so  the  parallelogram  is  correct. 

This  is  very  important,  that  the  tangents  have  the  correct  direc- 
tion, for  tlie  joints  are  made  square  to  tlie  tangents,  therefore  be 
rareful  to  give  the  tangents  the  right  angle  at  C,  for  they  control  the 
joints. 

Draw  the  chord  AG;  bi.sect  AG  at  D:  bisect  DA  and  DG 
at  E  and  F;  bisect  AE  and  EG  at  J  and  H.  From  A,  J,  E. 
F,  H  and  G.  draw  ordinates,  indefinite  and  parallel  with  the 
director  OC,  Now  transfer  the  points  2,  3.  4,  &c.  on  the  ordinates 
on  plan.  Fig.  1,  to  the  corresponding  ordinates  on  face-mould. 
Make  A  5  and  A  6,  also  G  7  and  G  8,  each  ecpial  Jl2,  in  eleva- 
tion. Fig,  2.  Now  trace  the  curve  through  the  points  .5,  2,  7,  &c., 
lor  ti\e  concave,  and  through  the  points  6,  4,  8.  etc.,  for  the  con- 
vex side  of  face-unmld  using  a  pliable  strip.  Make  the  joints  at 
A  and  G  square  to  the  tangents  AC  and  GC;  the  sections  at  M 
and  N  represent  the  joints  at  A  and  G;  the  tangents,  after 
being  transferred  from  the  mould  to  the  face  side  of  crook.  They 
are  then  squared  over  the  joints  as  shov.ii  at  M  and  N;  the  dotted 
lines  indicate  gauge  lines  for  centering  the  plank.  The  bevel 
found  in  the  angle  at  P,  Fig.  2,  is  a)ii)lied  throniih  the  center, 
tlien  the  block  pattern  is  applied  square  to  the  line  made  fronx 
the  bevel,  as  shown. 

Observe  the  bevel  at  M  as  ai)])lied  will  iiitcli  the  joint  at  G 
up,  and  the  bevel  as  applied  at  section  N  will  pitch  the  joint  at 
A  down. 

The  shadetl  ])arts  show  the  amount  of  over  wood  at  the  joint.s 
that  has  t<j  V)e  removed,  and  also  the  width  re<|uired  at  th«  joints 
to  saw  out  the  crook  a  sufficient  width  and  fhirkness  to  <'Oiitaiu 
the  twist  of  wreath  i)iece.  At  tiie  points  2,  4.  on  the  <lirector, 
the  section  of  rail  is  square  to  the  face  of  crook.  Hence,  at 
iiial  point  the  bevels  blend,  and  the  width  of  face-mould  is 
equal  to  the  true  width  of  rail.  At  that  point,  enough  over 
wood  on  the  convex  side  to  dress  olf  the  saw  marks,  is  all  that 
is  re(|uired,  but  on  the  concave  side,  owing  to  the  curvature 
of  rail  section,  more  or  less  is  required  to  saw  out  the  crook; 
for  a  deep  rail  and  a  small  cylinder  tlie  increa.sed  width  will  bo 
greater,  as  the  depth  of  rail  decreases,  and  the  diameter  of  cylinder 
increases,  the  amount  of  over  wood  at  the  normal  line  decreases. 
In  most  cases,  half  inch  will  be  sufficient  on  the  concave  side. 

Pig.  4.  Exhibits  an  isometricul  ideio  of  the-  solid  to  fuircc 
v:lth  th-e  plan  Fig.  1  and  elevation,  Fig.  2;  and  is  intended,  not 
as  a  working  drauring,  hut  to  lead  the  student  in  Imnd-railing  to 
study  the  prismatic  solid,  for  in  that  the  learner  unll  see  the  rea- 
son ivhy,  for  every  line  sooner  than  by  any  other  method. 


48  rLAiK  9.  —     - 

The  plan  or  end  of  solid  is  represented  by  the  parallelogram 
OACJB.  From  the  center  O,  draw  the  center  line  of  rail  ASB; 
make  BG  equal  the  height  BG,  Fig.  2;  let  CiJ  and  OO  equal 
the  height  CH,  Fig.  2,  connect  HA  and  OA,  also  connect  GO 
and  Gil;  for  the  parallelogram  OAHG  on  the  cutting  plane, 
standing  over  the  horizontal  plane  OACB  as  shown. 

The  diagonal  OC  is  the  director  on  (he  horizontal  plane  which 
bisects  the  chord  AB  at  D;  bisect  AD  and  DB  at  E  and  F. 
From  E  and  F  draw  ordinates  parallel  with  the  director  DC,  to 
intersect  the  center  Une  ASB  at  o  S  and  3.  The  chord  AG  on 
the  cutting  plane,  stands  directly  over  the  chord  on  the  horizontal 
plane  OACB,  as  shown. 

Bisect  the  chord  AG,  on  the  cutting  plane  OAHG;  at  J, 
bisect  JA  and  JG  at  K  anil  L;  draw  the  diagonal  OH  for  the 
director  on  the  cutting  plane. 

From  K  and  Z/  iliaw  ordinates  indefinite  ;  Jiow  transfer  the 
l>oints  o,  S,  o,  from  the  ordinates  on  1  lie  horizontal  plane  to  the 
(•orres]»onding  ordhiates  on  the  cutting  jiiane  at  4,  4,  4  ;  then  trace 
the  elliptic  curve  through  the  points  A,  4,  4,  4.  G,  for  the  center 
Hue  of  rail. 

If  a  bevel  as  shown  at  M  be  applictl  square  to  the  inclination 
AO,  both  on  the  side  of  solid  and  over  the  cutting  jdane,  it  will  be 
found  to  agree  with  the  bevel  found  at  P,  Fig.  2,  and  may  be  used 
by  the  beginner  to  prove  the  bcA'els  found  in  the  usual  way  before 
applying. 

The  sides  of  the  block  are  marked  for  cutting  with  the  bevel, 
taken  from  the  angle  AHC,  Fig.  2,  and  is  applied  as  shown  at  H, 
Fig.  4,  on  all  four  sides. 

!^ig.  5.  Exhibits  the  .slkliivj  of  the  nundd  to  confonn  to  the 
hcvcls  in  the  fornidtion  of  the  wrcoth-piccv.  The  heavy  ciuved 
line  indicates  the  crook  as  sawed  from  the  )>lank.  The  face  of 
crook  must  be,  carefully  dressed  out  of  wind,  where  there  is  steam, 
this  is  (luickly  done  on  a  hand  jointei';  then  if  the  face-mould  b(; 
made  of  wood  test  the  (iorrectness  of  joints  by  aj)plying  the  stf>ck 
of  s(luar(^  to  the  joint  and  the  blad(!  to  the  tangent.  If  correct, 
place  th(5  face-mould  in  Uw.  center  of  ci'ook  and  tack  a  brad  at  each 
end  to  incveiit  th(>  mould  from  shifting;  then  mark  the  joints,  also 
nuirk  the  position  of  tangents  AD  and  BD  on  the  crook  from  the. 
mould,  also  the  nornial  line  4  2,  then  lift  the  mould  and  complete 
the  marking  of  tangents  and  the  normal. 

Now  cut  and  dress  olf  the  joints  square  to  the  face  of  crook, 
and  also  S(iuare  to  the  tangents,  then  carry  the  tangents  across  the 
joints  sipiare  lo  the  face  of  crook  as  shown  by  the  lines  2  :>,  at 
sections  JW  and  JV;  also  inark  the  tangents  AD  and  BD  on  the 
opposite  side  of  crook  s(|uare  to  the  joints. 

Then  center  tht;  plank  with  the  gauge  as  shown  by  the  dotted 
lines  intersecting  tiie  lines  2  o,  at  hh ;  then  through  the  inter- 
section aiiply  the  bevel  at  M  and  the  reverse  way  at  section  N,  so 
as  to  have  the  l)evels  cross  the  tangents. 

A))])ly  the  block  ])altern  square  to  the  line  (>  7,  made  from  the 
bevel,  showing  tlie  twist  of  wreath-piece  in  the  rough  crook  ;  now 
make  AC  and  BE  on  the  upper  side;  of  crook,  etiual  2  (5,  on  the 
section:  draw  CD  and  ED  parallel  to  AD  and  SZ),  repeat  the 
same  on  the  lower  side  of  crook  ;  HD  and  FD  is  parallel  to  AD 
and  BD. 

Now  slide  the  face-moulil  so  as  to  agree  with  the  tangents  on 
the  crook  ;  tangeids  ad  and  bd  on  the  mould  must  lie  over  tan- 
gents CD  and  ED  <m  the  crook  ;  when  in  the  right  position  tack  a 
brad  at  each  end  to  hold  the  mould  in  place,  then  scribe  around 


Platk  10.  49 

tliat  portion  of  mould  that  lies  over  the  crook  including  tlie  joint. 
Also  marli  the  minor  axis  5  8,  on  the  upper  side  of  crook  ;  repeat 
this  operation  on  the  lo^Yer  side  as  shown  by  the  dotted  lines. 

It  v.'ill  be  seen  now  from  the  position  of  tlie  two  moulds  and 
the  bevels,  tlic  formation  of  the  wreath  rail  in  the  crook,  a  line 
from  10  on  the  lower  side  of  crook,  to  S  on  the  upper  side,  gives  the 
direction  to  liold  the  tools  when  taking  the  surplus  wood  from  the 
concave  side  of  wreath-piece. 

At  sections  ilf  and  N  the  over  wood  is  shovra  removed  from  the 
concave  side.  As  the  joints  are  made  at  the  spring  liner,  to  connect 
other  wreath-pieces,  it  will  be  observed  the  block  jiattein  does  not 
give  the  correct  outline  of  the  sides  of  rail  section  as  sliown  by  the 
dotted  curved  lines  ;  but  it  the  joint  were  to  connect  with  straight 
rail  at  tlie  ujiper  end,  then  the  block  pattern  will  give  'bo  correct 
outline  for  tlie  lower  half  of  rail  section,  while  the  v.pper  half 
would  be  cuived.  And  also  at  joint  A  the  upper  half  would  be 
straight  and  the  lower  lialf  curved  ;  for  tliis  reason  \vhen  the 
wreath-piece  has  to  connect  an  easement  or  straight  rail,  there 
should  be  straight  wood  added  on  for  shank  e(]ual  to  Eb  'v:  Ca,  the 
distance  that  the  mould  slides  from  the  joint ;  the  shaded  part 
indicates  the  face  side  of  crook. 


PLATE  10. 


Plate  10.  [Scale,  IK^^-zl/].  Exhibit.-^  the  (■■  m .ilniclion 
of  the  face-mould  f(jr  <i  wrcath-piccc  hav'uKj  a  full  ai-uiuj,  ivlicn 
the  sc(jmciit  oil  plan  is  less  than  d  quarter  circle ;  in  thin  case 
the  angle  of  tamjents  on  planiviU  he  obtuse.  " •".     . 

Fig.  1.     Shmvs    the  plan.       Let   OA,    OB  be  the  radii; 

[lO^^J  draw  the  tangents  AC  and  BC  at  rigl;t  auK'hi  to  tlie  radii, 
creating  the  obtuse  angle  at  C,  draw  AR  and  BR  parallel  with 
tlie  tangents  BC  and  AC,  forming  the  (Idiombus)  i)aralleloKram 
RACB  on  plan.  Drav/  the  center,  concave  and  convex  sides  of 
rail  from  the  center  O;  prolong  the  tangenl  jBCindennite.  From 
A  and  .square  to  BC  {)roloiiged,  draw  AS  1  jr  the  base  of  bevels. 

Fig.  2.  Exhibit'^  the  development  of  tanuents  In.  elevation 
from  plan.  Draw  XX  for  a  base  line.  IMake  BC  and  CA  e(iual 
BC,  CA  on  plan.  Fig.  1,  draw  perpendiculars  at  A,  C  and  B 
from  the  l)ase  line  XX. 

Now  as  tlui  wreath-piece  is  to  have  a  full  easing,  one  of  tlie 
tangents  must  be  level  or  horizontal,  and  the  other  inclining.  We 
will  allow  tangent  AC  to  be  level,  and  lujnce  becomes  the  direct- 
ing ordinate  and  tangent  CB  will  be  inclining. 

Let  it  be  observed  also  that  when  tlie  cylindrie  .section  on  plan 
is  less  than  a  quarter  circle  and  a  full  easement  is  required,  as  in 
this  case,  then  two  bevels  Vv'ill  l»e  reciuired. 

Assume  DB  to  be  tlie  height  the  wreath-piece  is  required  to 
raise,  draw  DC  prolonged.  Make  CS  equal  CE,  Fig.  1.  Make 
BG-  equal  the  chord  BA,  on  plan.  Make  .BJ" equal  the  diagonal 
RC,  Fig.  1 ;  draw  EK  s(iuare  to  DC. 

Bevels.  Return  to  plan.  Fig.  1.  As  the  tangents  on  plan, 
Fig.  1,  are  both  the  same  length,  the  bevels  for  the  two  joints  will 
have  one  base,  A-E,  Fig.  1.  Make  EF  equal  EK,  Fig  2.  Let 
EH,  Fig.  1,  equal  the  height  BD,  Tis.  2.  Join  FA  and  HA,  for 
the  bevels  as  shown.  Parallel  with  BH,  draw  the  half  width  of 
vail  [IK^'G  cutting  the  hypotheuuse  of  bevels  at  L  and  M. 


50  Plate  10. 

The  full  width  of  rail  is  drawn  ou  ground  plan,  fer  the  pur- 
pose of  using  ordinates  in  tracing  the  face-mould.  Draw  the 
chord  AB  ou  plan.  Bisect  AB  at  G;  bisect  GB  and  GA  at  J 
and  K;  bisect  KA  at  N.  From  the  points  JST,  K,  G,  J"  and  B, 
draw  ordinates  parallel  to  the  director  AC,  cuttiug  the  concave, 
center  and  convex  lines  of  rail,  at  3,  3,  4,  &c. 

Fig.  3.  Exhibits  the  Facc-numld*  Make  DC  equal  DC, 
Fig.  2.  With  Z)  as  a  center  and  DG,  Fig.  2,  for  a  radius,  draw 
arc  at  A;  with  C  as  a  center  and  tangent  AC,  Fig.  1,  for  a  radius, 
draw  arc  intersecting  at  A,  connect  AC.  Parallel  with  CA  and 
CD,  draw  DB  and  AB,  creating  the  [Rhomboid]  parallelogram 
BACD,  on  the  cutting  plane,  or  plaue  of  plank. 

Proof.  The  diagonal  BC  must  equal  JD,  Fig.  2,  if  so,  the 
angle  of  tangents  at  Cis  correct. 

Draw  the  chord  AD.  Bisect  AD  at  G;  bisect  GD  and  GA 
at  J"  and  K ;  bisect  KA  at  M.  From  the  points  M,  K,  G,  J"  and 
2?,  draw  ordinates  indefinite  and  parallel  with  the  director  AC. 
Now,  from  the  ordinates  on  plan,  Fig.  1,  transfer  the  points  2,  3 
and  4,  to  corresponding  ordinates  ou  face-mould.  Fig.  3,  using  the 
chord  lines  as  a  base. 

Make  joints  at  A  and  D  square  to  the  tangents  AC  and  DC. 
Make  A  5  and  A  6  each  equal  HL,  Fig.  1 ;  also  make  D  7  and  D 
8  equal  FM,  Fig.  1 ;  then  tracts  the  curve  through  the  points  5, 
2,  7,  for  the  concave  side,  and  tlu'ough  the  points  6,  4,  S,  for  the 
convex  side  of  face-mould,  using  a  flexible  strip. 

The  section  at  P  shows  the  tangent  AC  squared  over  the 
joint;  the  dotted  line  indicatt-s  a  gauge  line  for  centering  the 
plank,  and  the  bevel  taken  from  the  angle  at  H,  Fig.  1,  is  applied 
from  the  face  of  crook,  tlirough  the  intersection  at  P  for  tlie  center 
of  rail ;  then  the  block  pattern  is  applied  square  to  the  bevel,  giviiig 
the  squared  section  of  rail  on  the  joints. 

The  section  at  R  repeats  tlie  operation ;  the  bevel  is  taken 
from  the  angle  at  F,  Fig.  1,  and  applied  from  the  upper  or  face 
side  of  crook.  Note  the  bevels  in  this  case,  do  not  cross  the  tan- 
gents ;  let  the  eye  start  at  A  and  follow  the  tangents  around  to  D; 
it  will  be  seen  tlie  bevels  both  point  to  the  right  of  the  tangents. 

The  reason  the  bevels  do  not  cross  is  because  the  minor  axis  is 
not  in  the  face-mould  but  away  beyond  to  the  riglit.  To  econo- 
mize room  we  have  made  use  of  the  ordinates,  but  if  the  trammel 
or  rod  be  preferred,  then  from  A  draw  a  line  indeiinite  and  at 
riglit  angles  with  tangent  AC;  then  prolong  the  diagonal  CB  to 
intersect  the  line  from  A  at  O.  Now  OA  will  be  the  length  of  the 
semi-major  axis  for  the  center  line  of  rail.  And  at  right  angles  to 
OA  will  give  the  direction  of  the  semi-minor  axis,  which  is  always 
equal  to  the  radius  of  the  circle  on  plan ;  draw  the  radial  line  OD 
indefinite ;  from  the  points  7  and  8,  draw  lines  parallel  to  tangent 
CD,  cutting  OD  at  9  and  10,  for  the  point  of  tangency  or  the  con- 
nection of  the  straight  with  the  curved  part ;  0  and  10  are  tlie 
points  through  which  the  elliptic  curve  will  pass,  f 

*  When  proceedint?  to  drav/  the  face-mould,  always  take  the 
lonj^est  tan<,'eut  with 'the  dividers  Orst;  this  will  be  found  the  most 
correct  and  economical  way. 

t  Let  it  be  observed  that  for  all  cylindric  sections  on  plan  Uas  or 
iircntcr  than  a  quarter  circle,  the  increased  width  of  mould  at  tlie  ends 
iiiay  be  laid  olf  from  the  joint  bevels,  but  not  correct,  only  when  the 
ioint  is  parallel  to  the  axis  of  the  cylindric  section,  as  at  .loiiit  4or 
when  the  tangent  is  level  as  yiC;  the  accoDii)anyinj,'  bevel  is  shown 
at  H.  Vv^.  I.  and  applied  at  section  P  Vv^.  :$.  But  not  conre)^  when  the 
tJingent  is  inclining,  as  CD,  in  elevation.  'Die  points  7  and  S  at  .loint 
D,  Fig. :{.  are  not  the  correct  points  through  which  tlie  elliiil  iiMmrye 
will  pass.  Tlie  points  will  be  outside  the  curve,  and  the  point  ,  will 
be  inside  the  curve.  The  points  !t  and  10  ou  the  rudial  Ime  01)  are  the 
correct  points.    See  Fig.  3,  Plate  11. 


Plate  10.  51 

Fig.  4.  Exhibits  an  isometrical  ijrojeetion  of  the  Prismatic 
Solid. 

The  rhombus  ACBR  shows  the  plan,  and  agrees  with  the 
parallelogram  RACB,  on  plan,  Fig.  1,  and  indicates  the  end  of 
a  block  resting  on  a  horizontal  plane  ;  BD  shows  the  height,  con- 
nect DC.  DS  is  parallel  with  AC  and  SA  is  parallel  with  CD, 
thus  indicating  the  rhomboid  on  the  cuttiug  plane  or  plane  of 
plank.     The  diagonal  CR  is  prolonged  equal  to  CO  on  plan.  Fig. 

1,  from  which  the  center  line  of  rail  ANB  is  drawn ;'*CBZ>, 
SRA  and  BDSR  show  three  sides  of  tlie  prism;  AB  is  the 
chord  lino  on  plan,  and  AD  shows  the  chord  on  the  cutting 
plane ;  tlie  shaded  part  ABD  shows  the  block  to  be  divided  on 
the  chord  plane,  thus  separating  the  prism  into  two  triangular 
prisms. 

Bisect  the  chord  AB  on  the  horizontal  iilane  at  G;  bisect 
GA  and  GB  at  K  and  J;  IMsecL  KA  at  M.  From  M,  K,  G 
and  J"  draw  ordinates  parallel  to  the  director  AC,  to  intersect  the 
center  line  ANB  at  o,  3,  8,  3.  !Now  draw  perpendiculars  on  the 
chord  plane,  dividing  the  cliord  AD  on  the  cutting  plane  ]>ropor- 
tiouately  with  the  chord  on  the  horizontal  plaue  at  the  points  2,  3, 

2,  2  ;  draw  the  ordinates  2  4.  2,  4,  &c.,  parallel  with  the  director 
AC,  and  equal  to  M  3,  K  3,  &c.;  then  trace  the  elliptic  curve 
through  the  points  D,  4,  4,  4,  4,  A,  using  a  pliable  strip.  To 
find  the  center  of  the  ellipse,  prolong  the  diagonal  C/Sto  intersect 
a  perpendicular  line  from  O  at  P;  then  PA  indicates  the  direc- 
tion, and  also  the  semi-major  axis.  From  P  and  square  to  PA, 
gives  the  direction  of  the  minor  axis. 

The  student  in  stair-building  should  take  great  interest  in  the 
study  of  these  solids. 

Let  him  first  prepare  the  solid  to  agree  with  the  parallelogram 
ACBR,  on  plau,  and  5'^  or  iV^  long;  divide  it  on  the  chord  plane 
ADB,  then  dowel  them  together,  and  cut  to  the  required  pitch. 
If  he  adds  the  sections  ARO  and  BRO,  forming  the  trapezium 
ACBO,  and  cutting  tliem  all  off  to  ihe  cutting  plane,  he  will 
liave  the  length  of  the  semi-major  axis,  AP  and  the  radial  line 
DP,  fur  Ihe  point  of  contact,  and  by  adding  anotlier  triangular 
piece,  BQO  [Q  is  not  shown],  and  cutting  it  off  to  tlie  same 
plane,  he  will  have  the  lengtli  of  the  semi-minor  axis  PT,  wliich  is 
plund)  over  OQ  on  tlie  horizontal  plane,  and  is  always  equal  to 
the  radius  of  the  circle.  If  the  student  will  apply  his  mind  to  the 
study  of  these  solids,  he  will  soon  master  the  most  intricate  prob- 
lems in  hand  railing. 

"  Fig.  5.  Shoics  the  aiipUcaiion  of  the  Face-mould  to  the 
Crook. 

The  heavy  line  shows  the  crook  as  sav/ed  out  from  thn  plank* 
After  the  crook  is  taken  carefully  out  of  wind  on  tlie  face  side' 
apply  the  face-mould  in  the  center  ;  nuirk  the  joints  at  A  and  D> 
also  the  tangents  AC  and  DC.  Now  lift  the  mould,  and  liiii.-,h 
marking  the  tangents,  whicli  should  be  eandully  transf(;rred  from 
the  face-mould  to  the  crook,  as  shown  by  the  heavy  lines  AC  and 
DC.  Next,  line  the  joints  A  and  23,  cut  and  dress  IJieiu  square 
to  tlie  face  of  crook,  and  tlie  tangents  ;  then  square  the  tangents 
across  ihe  joints  as  shown  by  the  ruies  2  ?>,  at  sections  P  and  R, 
Now,  center  the  plank  with  the  gauge,  and  thnuigh  the  iidcrsec- 
tion  made  by  the  gauge,  apj»ly  the  bevel  G  7.  Then  set  the  block 
pattern  sfpiare  to  the  line  6  7,  and  scribe  around  llit;  pattern 
showing  the  twist  of  ureal li-piec(!  at  the  joints.  Now  the  distajice, 
2  0  and  3  7,  is  what  the  mould  lias  to  slide  at  the  joints,  to  carry 
the  lines  of  twist  correctly  from  end  to  end  of  the  crook.     At 


5^'  Plate  10. 

joint  A,  let  AB,  on  the  upper  side  of  crook  equal  2  6,  at  section 
P;  and  AE,  on  the  lower  side  of  crook  equal  3  7,  at  section  P. 
Then  parallel  with  tangent  AC,  draw  BC  on  iue  upper  side  of 
crook;  and  parallel  with  AC,  on  tlie  lower  side  of  crook,  draw  EC. 

It  will  be  observed  that  £C  cannot  be  drawn  on  the  crook, 
but  the  mould  is  shifted  down  so  that  the  tangent  ac  on  the  face- 
mould  will  agree  with  the  center  line  6  7,  as  shown  at  section  P. 

At  joint  D  make  DH,  on  the  upper  side  of  crook,  equal  2  6, 
at  section  R;  and  DF,  on  the  lower  side  of  crook,  equal  3  7,  at 
section  R.  Now,  parallel  with  DC,  on  the  upper  side  of  crook, 
draw  HC;  and  parallel  with  tangent  DC,  on  the  lower  side  of 
crook,  draw  FC.  The  tangents  are  now  marked  on  the  crook, 
ready  to  apply  the  mould,  which  must  lay  over  these  lines,  havinej 
the  tangents  ac  and  dc  to  agree  with  the  tanarents  JBCand  HC, 
on  the  upper  side  of  crook  ;  and  tangents  EC  and  FC,  for  the 
lower  side  of  crook,  in  this  case,  the  sliding  of  the  mould  will  be 
easily  done,  for  the  line  of  joint  A  is  the  line  of  the  major  axis  of 
the  ellipse,  and  thus  becomes  a  slide  line  for  the  joint  of  face- 
mould,  if  correctly  made. 

If  the  face-mould  is  made  from  wood,  it  is  well  always  to  test 
the  correctness  of  the  joints  before  making  the  joint  on  the 
crook,  by  applying  the  stock  of  the  try-square  to  the  joint  and 
the  blade  of  square  to  the  tangent,  on  the  mould. 

The  face-mould  as  shown  is  shifted  so  that  the  tangents  ac 
and  dc  agree  v/ith  the  tangents  JSCand  HC,  on  the  upper  side 
of  crook,  and  while  in  this  position  scril)e  around  the  convex  side 
of  mould.  In  the  same  manner  slide  the  mould  on  the  lower  side 
of  crook  until  the  tangents  ac  and  cd  will  agree  with  the  tangents 
£?Cand  FC,  then  scribe  around  the  concave  side  of  mould. 

The  dotted  lines  at  section  R  show  the  sides  of  rail  section 
curved,  while  at  section  JPthe  block  pattern  gives  the  true  profile 
of  rail  section,  because  the  tangent  AC  is  level,  and  the  joint  is 
square  to  the  tangent ;  hence  the  plane  of  joint  is  parallel  to  (iie 
axis  of  the  cylinder.  The  joint  at  D  is  oblique  to  the  axis  of 
cylinder,  because  the  joint  is  made  square  to  the  tangent  DC, 
wliich  is  inclining. 

Itwill  be  noticed  at  J" and  K,  on  section  P,  that  there  is  a 
great  saving  of  material  in  cutting  out  tlie  crook  .square  to  t!io 
face  of  plank.  This  want  at  J" prevents  the  profile  of  moukl  on 
ils  concave  side  being  transferi-ed  to  the  face  of  crook,  by  tacking 
the  mould  to  the  crook  in  its  proper  ])Osition,  the  lower  arris  of 
mould  as  shown  supplies  this  want,  for  the  upper  side  of  crook. 
On  the  lower  side,  we  have  the  scrilje  line  complete  for  the  concave 
side.  After  working  off  the  surplus  wood  from  the  concave  side 
of  -wreath-piece,  then  use  the  Cui)per  gauge,  and  gauge  the 
wreath-piece  to  a  parallel  width  ;  then  dress  off  to  the  gauge  line; 
the  bevel  at  joint  A  gives  the  direction  to  guide  the  tools,  or  a  line 
from  the  edge  mould  through  the  center  of  plank  at  joint  D, 
will  give  the  direction. 

For  the  twist  line,  use  a  pliable  strip  and  apjdy  it  to  the  top 
side  of  v.'reath-piece  on  the  concave,  and  also  on  the  convex  sides, 
to  agree  with  the  block  pattern  at  the  joints.  vVfter  tracing 
carefully  the  twist  line,  remove  the  surplus  wood  from  the  upper 
side  of  wreath-piece,  then  gauge  for  the  depth. 

While  gauging  for  the  depth  the  gauge  will  helj)  to  detect 
any  abrui>t  places  in  squaring  the  ui)per  side  of  wreath-piece, 
especially  when  there  is  a  want  of  wood  on  tlu;  arris  of  wreath- 
piece  as  is  often  the  case.  If  there  be  .several  wreath-pieces, 
ramps  or  easements  connected,  bolt  them  all  together  before 
applyhig  the  thin  strip  for  the  falling  line  of  rail. 


Plate  U. 


PLATE  II. 

Plate  11.  [Scale,  \}i'^=V[.  Exhibits  the  construction 
of  the  face-mould  for  a  u-rcath-piece  havinrj  an  intermediate 
easing,  alien  the  cyllndric  section  on  plan  is  less  than  a  quarter 
circle. 

Fig.  1.  Sliows  the  cyUndric  section,  the  radius  OA,  for  the 
center  line  cqucds  14^\ 

From  the  center  O  draw  the  center  line  of  rati  ASB.  As 
orclinates  will  be  iised,  draw  the  full  width  of  rail,  dividing 
equally  on  each  side  of  the  center  line. 

From  A  and  B  draw  the  tansreuts  ACand  BCperpendicular 
to  the  radial  linos  OA  and  OB.  Farallel  with  CA  and  CB 
draw  BL  and  AL,  forming  the  parallelogram  ZiACB  on  plan. 
Prolong  tangent  JBC  indefinite.  From  A,  and  at  right  angles  to 
BC,  draw  AD,  the  seat  line  for  bevels. 

Pig.  2.  Exhibits  the  development  of  tangents  from  plan 
Fig.  1.  As  this  loreath-jyiece  is  to  have  an  iyitermediate  easing, 
both  tangents  vnll  be  inclining,  but  each  loill  be  different  in  their 
inclination.     AjhI  also  two  joint  bevels  ivill  be  required. 

Let  XX  indicate  the  edge  of  drawing  board,  and  BC,  CA 
equal  the  tangents  JBC  and  CA  on  plan,  Fig.  1;  from  which  erect 
perpendiculars  to  XX.  as  shown. 

Assume  CD  to  be  the  height  that  the  tangent  AC  on  plan, 
has  to  raise.  Draw  AD  prolonged  to  intersect  the  perpendicular 
from  JBat  F.  Again  assume  BE  to  be  the  height  of  both  tan- 
gents, draw  ED  prolonged  to  intersect  the  base  line  XX  at  G. 

From  E.  and  parallel  to  XX,  draw  EH,  cutting  the  perpen- 
diculars from  A  and  C  at  i?  and  J:  malce  CK  and  JL  eacli 
equal  CD  on  plan,  Fig.  1.  From  K,  and  perpendicular  to  DG, 
draw  KM.  From  L,  and  square  to  AF.  draw  LN.  Make  EP 
equal  tlie  diagonal  CL  on  plan.  Let  EQ  equal  the  chord  AB 
on  plan,  Fig.  1. 

Bevels.  Eeturning  to  the  plan,  make  DF  equal  MK,  Fig. 
2,  and  JJi?  on  plan,  equal  LN,  Fig.  3;  draw  J'A  and  HA  for 
the  bevels  required,  as  shown. 

Parallel  with  BiJdraw  the  half  width  of  rail  [IK''''],  cutting 
the  bevels  at  Y"  and  X, 

As  the  face-mould  in  this  case  is  traced  by  the  use  of  ordi- 
nates,  first  find  their  direction  on  plan.  Fig.  1. 

Make  BJ"  equal  CG,  Fig.  2;  draw  JL  for  the  director;  join 
AB  for  the  chord.  Bisect  the  chord  AB  at  Q:  bisect  QA  and 
QB  at  JWand  N;  bisect  AM  at  P.  From  A,  P,  M,  Q,  iVand 
B  draw  ordinates  parallel  with  the  director  LJ  to  cut  the  con- 
cave, center  and  convex  sides  of  rail  at  the  points  2,  3,  4,  &c. 

Fig.  3.    Exhibits  the  facc-moidd. 

Make  EDG  equal  EDG,  Fig.  2,  with  .E7  as  a  center,  and 
BQ  Fig.  2,  for  a  radius.  Draw  arc  at  A,  then  with  D  for  a 
center,  and  DA,  Fig.  2.  as  a  radius,  draw  arc  intersecting  at  A. 
Join  DA.  Parallel  with  DA  and  DE,  draw  EL  and  AL,  estab- 
lishing the  parallelogram  LEDA  on  tlie  plane  of  plank,  which 
will  agree  with  the  parallelogram  LACB,  Fig.  1,  when  in 
position. 

Proof.  The  diagonal  LD  must  equal  the  distance  PF,  Fig. 
2,  join  CfA  for  tlie  director.     Draw  the  joints  at  A  and  E  square 


64  Plate  11. 

to  the  tangonts  AD  and  JSD;  draw  the  chord  AE.  Bisect  AE 
at  G:  l)isect  AG  and  BG  at  M  and  N;  bisect  AM  at  P.  From 
A,  P,  M,  G,  N  and  E,  lJra\v  ordinates  indefinite,  and  parallel 
to  the  director  AG. 

Now  transfer  points  2,  o  and  4,  on  the  ordinates,  Fig.  1,  to 
corresponding  ordinate  on  tlie  face-nionkl  as  shown,  nsing  the 
chords  for  base  lines.  Make  A  .5  and  A  6  each  eqnal  HX,  Fig. 
1,  make  E  7  and  E  8  each  eqnal  FY,  Fig.  1.  Now  trace  throngh 
the  points  for  the  concave,  center  and  convex  cnrves  of  face- 
monld.  Ilemember  the  points  5  and  6,  at  joint  A,  and  7  and  8,  at 
joint  E,  are  not  quite  correct,  and  would  not  do  to  set  the 
rod  or  trammel  by,  but  are  near  enough  for  the  practical  man, 
when  using  a  strip.  If  the  point  of  taugency,  or  the  connection 
of  straight  with  the  curved  part  is  required,  then  return  to 
plan,  Fig.  1.  Prolong  the  chord  at  A,  also  the  ordinate  4  A,  and 
draw  an  ordinate  from  the  joint  at  G.  Now  with  F  for  a  center, 
and  AP,  Fig.  3,  as  a  radius,  draw  arc  cutting  the  ordinate  at  5; 
draw  F  .5  prolonged,  to  intersect  the  ordinate  from  6  at  7.  Return 
to  Fig.  o,  and  make  A  1  equal  7  .5,  Fig.  1,  and  1  9  equal  6  *,),  Fig. 
1,  draw  9  10  through  A,  for  the  points  of  contact  for  joint  A.  Tlie 
points  for  joint  S'may  be  fouiid  in  the  same  way. 

If  the  center  O  be  required,  so  as  to  trace  the  face-mould 
with  the  trannnel  or  rod. 

Then  return  to  Fig.  2.  Make  ^V  equal  the  diagonal  OC, 
Fig.  1.  From  V  erect  the  perpendicular  to  intersect  FF  pro- 
longed, at  Y,  Now  prolong  the  diagonal  DL,  Fig.  3,  to  efpial 
.  YF,  Fig.  2,  at  O.  From  O,  and  parallel  with  the  director  AG, 
draw  OB,  equal  to  the  radius  OB,  Fig.  1,  for  the  semi-minor 
axis ;  and  a  line  at  right  angles  to  OB,  through  O,  will  be  the 
direction  of  the  major  axis.  Draw  the  radial  lines  OA  and  OE 
indefinite  ;  from  the  points  7  8  and  6  9,  on  the  joints,  draw  lines 
parallel  to  the  tangents,  to  intersect  the  radial  lines  at  a  8,  and  9, 
10  for  the  points  of  taugency,  through  which  the  elliptic  curve 
will  pass.*  The  mould  may  now  be  drawn  with  the  trammel  or 
straight-edge,  without  the  use  of  ordinates.  The  section  at  W 
shows  tlie  bevel  found  in  the  angle  at  H,  Fig.  1,  applied  from  the 
face  side  of  crook;  and  the  section  at  i?  shows  the  bevel  found 
in  the  angle  at  F,  Fig.  1,  applied  through  the  center  made  by  the 
intersection  of  the  gauge  line  witli  the  tangent  EH,  that  is 
squared  over  the  joint ;  the  bevel  line  governs  the  block  pattern. 
The  shaded  part  shows  the  surplus  wood  that  has  to  be  removed 
to  foj-m  the  twist  of  wreath-rail,  and  also  the  width  at  the  joint, 
to  saw  out  the  crook. 

Fig.  4.  Exlbihits  an  isometrical  view  of  the  prismatic 
solid  to  show  the  sLudent  the  combination  of  lines  in  perspective, 
(Did  the  paraUclocjnim  on  the  cutilag  phine  in  position  over  the 
p<t,r(dlcioijrain  on  tlie  horizontal  jjlonc. 

The  rhombus  ACBL  indicates  the  horizontal  section  of  solid 
and  agrees  with  tlie  parallelogram  LACB,  on  plan.  Fig.  1. 
ASB  shows  the  center  line;  AB,  the  chord  on  plan  ;  CD,  the 
height  of  lower  tangent,  and  BE,  the  height  of  both  tangents; 
connect  ED  and  DA.  Parallel  with  DE  and  DA  draw  AL  and 
EL,  for  the  parallelogram  ADEL  ou  the  cutting  plane,  which 
agrees  with  the  parallelogram  ACBL  on  the  horizontal  plane. 
Prolong  the  horizontal  line  BC  indefinite;  prolong  ED  to  inter- 
sect BC?  prolonged,  at  G,  establishing  the  poiut  G;  connect  GA 
for  the  director. 

*  These  correct  points  for  the  ta'aimuel  are  more  clearly  explained 
at  Fig.  3,  Piute  12. 


Plate  11.  55 

Bisect  the  chord  AJB  and  draw  the  ordinalcs  parallel  •with  the 
director,  to  intersect  tlio  curve  ASB,  as  shown.  From  the  chord 
on  plan,  erect  perpendiculars  to  intersect  the  chord  on  the  cutting 
plane,  from  which  draw  ordinates  parallel  with  the  director  AG; 
then  transfer  the  points  in  the  circle  on  the  horizontal  plane  to 
corresponding  ordinates  on  the  cutting  plane,  using  the  chords  for 
base  lines,  as  shown. 

To  save  room  on  the  drawing  board,  VL  may  be  drawn  for 
the  director  within  the  parallelogram  by  making  ^V  equal  DG. 

By  applying  the  bevel  to  the  sides  of  the  solid,  and  over  on 
the  cutting  plane,  keeping  it  square  to  the  inclination  of  the  tan- 
gents as  shown  at  jP  and  H,  will  give  the  correct  bevels  for  their 
respective  joints. 

Fig.  5.    Shoivs  lioiv  to  slide  the  mould. 

The  heavy  line  indicates  the  crook  as  sawed  out  from  the 
rough  plank.  The  dotted  lines  parallel  with  joints  A  and  E, 
shows  the  over  wood  required  in  making  the  joints.  First  dress 
the  face  side  of  crook  carefully  out  of  wind,  then  center  the  face- 
mould  on  the  crook  and  carefully  mark  the  joints  and  position  of 
the  tangents.  Now  lift  the  mould  and  finish  marking  the  tan- 
gents AD  and  ED  on  the  face  of  crook ;  then  square  the  joints 
from  the  face.  Cut  and  dress  them  square  to  the  tangents  AD 
and  ED,  and  also  to  the  face  of  crook,  carry  the  tangents 
across  the  joints  square  to  the  face,  as  shown  by  the  line  2  3,  at 
sections  Q  and  R;  also  mark  the  tangents  AD  and  ED  on  the 
opposite  side  of  crook  square  to  the  joints. 

Now  center  the  thickness  of  crook  with  a  gauge  as  shown  by 
the  dotted  lines  at  sections  Q  and  R.  Through  the  intersection 
at  4,  4,  apply  the  bevel,  intersecting  the  upper  surface  of  crook 
at  6,  and  the  lower  side  at  7  ;  then  apply  the  block  pattern  square 
to  the  line  6  7,  given  by  the  bevel,  and  trace  the  profile  of  the 
squared  section  of  rail  on  the  joint,  showing  the  twist  of  the 
wreath-piece  at  the  joints. 

Now  3  6  is  the  distance  at  the  joints  the  face-mould  has  to 
shift  on  the  upper  surface  of  crook,  and  3  7  the  distance  on  the 
lower  side  of  crook ;  then  where  they  intersect  the  upper  and 
lower  sides  of  crook,  as  JB  and  C,  at  joint  A;  and  i^ and  G  at 
joint  E;  then  parallel  with  tangents  AD  and  ED,  draw  BD  and 
ED  for  the  upper  side  of  crook,  and  for  the  lower  side  of  crook 
draw  CD  and  GD,  parallel  to  AD  and  ED. 

Then  slide  the  mould  so  that  the  tangents  ad  and  ed  on  the 
mould,  will  coincide  exactly  with  the  tangents  BD  and  FD  on 
the  crook  ;  when  the  mould  is  in  its  correct  position,  the  joints  on 
the  face-mould  will  be  parallel  Avith  the  joints  on  the  crook. 
When  the  mould  is  in  the  correct  position,  fasten  to  the  crook  and 
scribe  around  the  mould,  and  also  the  joint  at  a,  so  that  when 
placing  the  mould  on  again,  to  work  otf  the  surplus  wood,  the 
mould  may  be  easily  adjusted. 

Now  arrange  the  mould  on  the  lower  side  of  crook  in  the 
same  manner,  as  the  tangents  ad  and  ed  on  the  face-mould  will 
agree  with  the  tangents  CD  and  GD,  on  the  crook  ;  then  scribe 
around  the  mould  and  the  joi)it  at  e.  The  face-mould  is  shown 
on  the  lower  side  of  crook  by  the  dotted  lines,  and  on  the  upper 
side  of  crook  by  the  light  solid  lines.  When  scribing  the  outline 
on  the  crook,  the  minor  axis  should  be  transferred  also  to  the 
crook,  on  both  sides  which  will  give  a  plumb  line  for  a  guule  to 
direct  the  tools  and  also  to  center  the  rail,  when  tracing  the  falling 
line  of  wreath-piece  ;  MN  shows  the  minor  axis  through  the 
center  of  crook,  5  8  on  top,  and  9  10  on  the  lower  side  of  crook. 


36  Plate  12. 


At  P  and  /S  the  surplus  wood  is  sliown  removed  from  the  con- 
cave side  ot  wreath-piece,  and  ready  to  gauge  for  the  convex 
side.  Between  the  two  face-moulds  at  6  and  7,  is  shown  the  cj'l- 
iudric  section  minus  the  triangles  at  J"  and  Li. 

The  profile  of  the  squared  section  of  the  rail  at  the  joints  A. 
and  J57  will  be  curved  as  shown  by  llie  dotted  lines  at  sections  Q 
and  R,  if  they  connect  other  wreath-pieces. 


PLATE  12. 

[Scale,  \yi"=^V.\  Exhihits  the  construction  of  the  face- 
mould  for  a  wrerith-piece  loithout  <in  cnshir/,  when  the  cylindrical 
section  on  2)laH  is  less  than  a  qua  rLcr  circle. 

..,  Fig.  1.  Shores  the  cylindrical  section  less  than  a  quarter 
Circle. 

The  radius  OB  equals  If/''.  Draw  the  center  line  ASB: 
draw  the  radii  OA  aud  OB;  draw  the  tangents  AC  atid  BC 
pen^endicular  to  the  radii :  set  off  on  each  side  of  the  center  line 
the  half  width  of  rail,  and  draw  the  concave  and  convex  sides. 
Parallel  v>'ith  tangents  CA  arid  CB,  draw  BL  and  AL,  and  we 
have  the  parallelogram  LACB.  on  i>Ian. 

Prolong  the  tangent  BC  io  the  left.  From  A,  and  at  right 
angles  to  jBC  prolonged,  draw  AD,  the  seat  of  bevel. 

Fig.  2.  Shmos  the  development  and,  elevation  of  tangents 
for  a  wreath-piece  loilhont  an  easing,  the  two  tangents  must  have 
Die  .same  inciinatioti,  arcd  only  onehcvcl  wLllbe required  for  both 
joints. 

Let  XJT  indicate  the  edge  of  drawing  board.  Make  J5C  and 
CA  each  etjual  tangents  .BCand  CA,  on  plan.  Fig.  1.  From  AC 
aud  B  erect  perpendiculans  to  xx.  Assume  BD  to  be  the  lieiijltt 
required  for  tli3  wreatli-pie:'e  to  raise,  draw  the  inclination  AD, 
■cutting  the  perpendicular  from  C  at  E.  Make  BF  ecpial  the 
chord  AS,  on  plan,  Fig.  1.  Make  CH"  ennal  CD,  oa  plan,  Fig.  ]. 
From  H,  and  perpendicular  to  AE,  dravv  HJ. 

Bevel.  At  Fig.  1.  make  DiJ  equal  JH,  Fig.  2,  connect  EA; 
parallel  with  EB,  draw  the  half  width  of  rail,  cutting  EA  at  F. 
Draw  the  rhord  AB,  and  diagonal  CL,  bisecting  AB  at  G;  bisect 
AG  and  GB  at  J" and  H.  From  A,  J,  iJand  B,  draw  ordinates 
to  intersect  the  concave,  center  and  convex  curves  of  tlie  cyliudric 
section  at  3,  55,  4,  «&c. 

Pig.  3.  Exhibits  the  Facc-mmdd.  Make  DE  equal  the 
tangent  DE,  in  elevation,  Fig.  2  ;  with  D  for  a  center,  and  DF, 
Fig.  2.  for  a  radius,  draw  arc  at  A;  again,  with  E  as  a  center, 
and  ED  for  a  radius,  draw  arc  intersecting  at  A,  Join  AE: 
parallel  with  EA  and  ED,  draw  DL  and  AL,  for  the  parallelo- 
gram LDEA,  that  will  agree;  with  the  parallelogram  LBCA,  on 
plan,  Fig.  1. 

Proof.  The  diagonal  EL  must  agree  with  the  diagonal  CL 
o:i  plan,  Fig.  1.  ]\Iake  joints  at  A  and  D  square  to  the  tangents 
ASa'id  DE ;  make  A  ;i  and  A  :'.,  also  D  4  and  D  5,  each  equal 
EF,  Fig.  1  ;  prolong  EL  to  O.  equal  to  the  diagonal.  CO,  Fig. 
].  Draw  the  radial  lines  OA  and  OD  prolonged.  From  ]>oints 
2  and  ?,,  al-o  4  and  .5.  draw  lines  parallel  to  the  tangents  AE  and 
BE,  to  intersect  the  radial  lines  at  the  points  a,  b  and  d,  h,  for 
the  points  of  contact. 


Plaxk  12.  57 

As  we  will  use  ordinates,  to  locate  points  in  the  curves,  draw 
chord  AD,  intersecting  the  diagonal  at  G.  Bisect  GA  and  GD 
at  t7  and  if.  From  the  points  A,  J",  jH"  aad  Z>,  draw  ordinates 
parallel  with  the  director  EJL  indefinite.* 

Now  transfer  the  points  on  ordinates,  Fig.  1,  to  corresponding 
ordinates  on  face-mould,  using  the  chords  as  Ijase  lines;  then  trace 
the  curves  through  the  points  2,  3  and  4,  for  the  inside,  center  and 
outside  of  face-mould,  using  a  llexible  strip. 

If  a  trammel  or  rod  be  preferred  to  trace  the  elliptic  curve  of 
face-mould,  then  pivot  the  trammel  at  O  witli  the  arms  at  right 
angles  to  the  semi-minor  axis  O  3,  as  shown  ;  set  from  pencil  to 
minor  pin  on  the  rod,  the  distance  O  ;3,  tor  the  concave  side  of 
mould,  then  place  the  pencil  in  point  a,  and  drop  the  pins  in  the 
grooves,  and  fasten  the  major  pin  ;  then  trace  the  curve  tluougli 
the  points  a,  2,  d.  For  the  convex  side  set  from  pencil  to  minor 
piu,  the  distance  O  4,  then  place  the  pencil  in  h;  drop  tiie  pins  in 
the  grooves,  and  fasten  tiie  major  pin,  and  sweep  the  convex 
curve. 

The  radial  lines  OA  and  OD  give  the  points  of  contact  or 
connection  of  straight  with  the  circular  part. 

The  sections  M  and  N  show  the  tangents  carried  over  the 
joints,  sijuare  from  the  face  of  crook ;  the  dotted  lines  indicate 
the  thickness  of  plank  centered  with  a  gauge.  The  bevel  is 
applied  from  the  face  of  plank  through  the  intersection,  and 
the  block  pattern  is  shov/n  applied  siiuare  to  the  bevel  for  the 
twist  of  rail  at  the  joints  ;  the  shaded  part  indicates  the  width  at 
the  joints  to  saw  out  the  crooks,  and  is  shown  by  the  dotted  lines 
5,  7,  9,  6,  8,  10.  at  the  face-mould. 

At  the  normal  line  7  S,  %"  on  the  convex  side,  and  %"  on 
the  concave,  is  all  the  over  wood  that  will  be  required  to  saw  out 
the  crook  at  that  point,  as  the  section  of  rail  at  this  point  is 
always  square  to  the  face  of  plank,  and  the  width  of  face-mould 
at  this  point  is  always  equal  to  the  true  width  of  rail. 

When  marking  out  the  crooks,  lay  down  tlie  face-mould  on 
the  plank,  set  olf  on  each  side  of  the  joint  the  amount  that  llie 
crook  has  to  be  wider  tiian  the  face-mould,  as  A  G,  A  .5,  and  D  y, 
i?  10.  At  the  minor  axis  set  off  4  7  to  equal  %",  and  2  8  to 
equal  ^i.".  Now  shift  the  mould  from  3  to  5,  and  the  point  4 
move  to  7,  so  that  the  mould  will  cut  the  point  7  ;  after  n)arking 
the  [flank  from  h  to  7,  proceed  in  the  same  manner  to  mark  from 
t)  to  7  ;  repeat  the  operation  for  the  concave  side  from  10  to  S  and 
fj  to  8,  allowing  yi"  surplus  wood  to  make  the  joints  at  A  and 
JB,  as  shown. 

This  metiiod  saves  making  an  extra  mould  to  saw  out  the 
crook  which  is  unnecessary. 

Fig.  4.  Shon's  an  isometrical  perspective  of  the  solid,  and 
the  euttiwi  plmic  AEDL,  in  vosition  over  the  horizontal  plane, 
ACBL. 

ACBL  indicates  the  cud  of  block  resting  on  a  horizontal 
plane  and  agrees  with  the  parallelogram  ACBL  on  plan,  Fig.  I ; 
CE  is  the  height  of  the  lower  tangent,  and  BD  indicates  tho 
whole  lieight  of  both  tangents.  Join  DE  and  AE;  draw  DL 
and  AL  [farallel  with  EA  and  ED.  This  is  done  with  the  bevel 
set  to  the  angle  ADB,  Fig.  2.  Now  cut  the  block  to  these  lines, 
aiul  we  have  the  paiallelogram  DLAE  to  indicate  the  parallelo- 
gram laid  down  at  Fig.  3,  on  the  face-mould.     Now  prolong  BC 

*  Whenever  the  tangents  are  hoth  the  saiuo  inclination,  and  tlie 
same  Icnjxtli  in  elevation,  the  diaRonal  becomes  tJie  director,  and  is 
normal  to  the  curve,  and  on  it,  the  minor  axis  is  set  oil.  i 


58  I'LATE    13. 

indeGnite.  Prolong  DE  to  intersect  BC  prolonged,  at  G,  join 
GA  for  the  director  of  ordinates.  It  will  be  observed  now  that 
if  the  diagonal  EL  be  drawn,  it  will  be  parallel  with  the  director 
GA,  because  the  doited  line  EG  is  equal  io  DE.  This  is  always 
the  case  when  both  tangents  are  equal  on  plan  and  in  elevation, 
then  the  diagonal  LE  is  always  the  director  and  the  minor  axis. 

From  A  and  square  to  EG  draw  AH;  this  indicates  the  seat 
for  the  bevel  shown  at  AD,  Fig.  1.  From  jffand  square  to  EG 
draw  JIJ;  this  indicates  the  height  for  the  bevel  as  shown  at  HJ, 
Fig.  2.  JA  indicates  the  hypotlienuse  of  bevel  at  EA,  Fig.  1. 
The  same  bevel  is  found  direct  from  the  block  as  shown  at  K,  by 
applying  the  bevel  scpiare  to  the  inclination,  both  from  the  side  of 
block  and  from  the  cutting  plane. 

The  chord  lines  AB,  on  the  horizontal  plane,  and  AD,  on 
the  cutting  plane,  in  this  case  come  over  each  other,  so  that  the 
])erpend!culars  connecting  the  bisections  arc  not  shown  as  at  Fig. 
4,  Plate  11. 

To  show  the  point  for  trammel,  prolong  the  diagonal  CL  to 
O,  then  dowel  on  the  triangular  blocks  ALO  and  BLO,  and  cut 
them  olf  to  the  cutting  plane  DLAE.  We  will  then  have  the 
trapezium  DEAN,  shown  correctly  at  DEAO,  Fig.  3.  The 
point  iV  answers  to  the  point  O,  Fig.  3,  and  is  the  center  for  the 
trammel,  which  is  always  set  at  right  angles  to  N  3,  the  semi- 
minor  axis,  which  is  equal  to  the  radius  O  'i. 

Fig.  5.  Shows  the  manner  of  shifting  the  face-mould  on 
the  crouli. 

The  heavy  lines  show  the  crook  as  sawed  out  from  the  rough 
plank,  having  the  joints  A  and  D  cut  and  dressed.  Tin;  dotted 
lines  at  the  joints  show  the  K''^  of  over  wood  cut  away.  The 
shaded  part  indicates  the  upper  surface  of  crook. 

First  dress  olf  the  upper  side  of  crook  carefully  out  of  wind  ; 
place  the  face-mould  in  the  center  of  crook  ;  mark  the  joints  A 
and  B,  also  the  tangents  and  minor  axis  PQ  on  the  npjier  side. 
Now  lift  the  mould  and  complete  marking  the  tangents  Ai?  and 
DE,  on  the  upper  side  of  crook.  Now  S(iuare,  cut  and  dress  the 
joints  carefully,  by  applying  the  stock  of  square  to  the  joints  and 
the  blade  to  agree  with  the  tangents. 

After  the  jointing  is  done,  carry  the  tangents  across  the 
joints  square  to  face  of  crook,  as  shown  by  the  line  2  o,  at  sec- 
tions iVf  and  N;  and  also  square  the  tangents  from  the  joints  on 
the  opposite  side  of  crook.  Next  center  the  joints  at  4  with  a 
gauge,  as  shown  alike  at  both  joints  by  the  dotted  line.  Through 
the  intersection  at  4,  ap)>ly  the  bevel  0  7,  reversing  them  as 
bhown  at  sections  ilf  and  N. 

Apply  the  bh>ck  pattern  sciuare  to  the  line  G  7,  for  the  squared 
section  of  rail  on  the  joints,  showing  the  twist  of  wreath-piece. 

Now  i3  G  is  the  distan(;e  the  mould  has  to  shift  on  the  upper 
surface  of  crook  at  each  joint,  and  3  7  is  the  distanc(!  on  the  lower 
bide.  Then  make  A J[?  and  Di?  equal 'J  «  for  the  ujiper  side  of 
crook,  and  AK,  also  I?J'e<iual  3  7  for  the  lower  sUU'.  of  crook. 

Now  draw  BE  and  HE  paralUil  with  AE  and  DE ;  also 
draw  tangents  KE  and  JE  parallel  to  AE  and  DE  on  the  lower 
side  of  crook. 

Then  shift  the  face-mould  so  that  tangents  ae  and  de  will 
lay  over  the  tangents  BE  and  HE,  on  the  u))per  side  of  crook  ; 
when  the  mould  is  in  the  correct  position,  fasten  with  two  tacks, 
and  scribe  around  the  part  of  mould  that  lays  on  the  crook,  and 
also  at  the  joint.  Mark  the  minor  axis  5  8  on  the  upper  side  of 
crook.    Now  shift  the  mould  to  the  under  side  of  crook,  with  the 


Plate  13.  59 

tangents  ae  and  de  to  agree  with  the  tangents  KE  and  JE,  as 
shown.  Now  mark  around  the  edge  of  mould  and  the  joint  that 
remains  on  the  crool? ;  also  mark  the  minor  axis  9  10  for  the 
direction  to  hold  the  tools  when  removing  the  surplus  wood  from 
the  concave  and  convex  sides  of  wreath-piece. 

The  sections  at  M  and  N  show  the  over  wood  at  R  and  S, 
removed  from  the  concave  and  convex  sides  of  wreath-piece, 
showing  the  cylindric  section  containing  the  wreath-piece,  with 
the  least  possible  waste  of  material. 

By  tacking  the  mould  to  the  crook  the  arris  of  face-mould 
will  be  a  guide  to  dress  oft"  to  the  bevels  where  the  crook  is  cut 
away,  as  shown  at  XX,  &c. 

By  squaring  across  the  wreath-piece  at  P  and  Q,  and  the 
squared  lines  intersected  by  the  gauge,  as  shown  at  4,  will  give 
the  center  of  rail  to  regulate  the  falling  line  of  wreath-piece, 
and  by  drawing  a  line  from  10  on  the  lower  side,  to  8  on  the 
upper  side  of  crook,  will  give  the  direction  to  hold  the  tools  when 
removing  the  surplus  wood  from  the  concave  side  of  wreath- 
piece  ;  in  like  manner  9  5  gives  the  direction  on  the  convex  side. 

For  the  twist  or  falling  line  of  wreath-piece,  use  a  thin,  flex- 
ible strip,  bending  it  around  the  wreath-piece,  being  guided  at 
the  joints  by  the  corners  of  block  pattern,  and  the  depth  of  rail 
laid  ott'  at  the  crossing  of  the  minor  axis  ,•  the  eye  and  judg- 
ment must  guide  the  strip  between  the  joints  and  minor  axis. 

The  tangents  being  both  inclining,  and  the  joints  both  made 
at  the  spring  of  cylindric  section,  the  straight  lines  as  marked 
from  the  block  pattern  at  sections  M  and  N,  will  not  be  the  cor- 
rect contour  of  rail  section,  but  will  be  curved  as  shown  by  the 
curved  dotted  lines ;  for  this  reason  the  surplus  wood  at  the  joints 
on  the  concave  side,  should  not  all  be  removed,  but  left  full  so 
that  when  the  adjoining  wreath-piece  is  bolted  on,  they  both  can 
be  dressed  down  neat  to  the  required  curve  made  by  the  face- 
mould.  The  surplus  wood  may  all  be  removed  from  the  convex 
side,  as  the  block  pattern  on  that  side  allows  a  surplus  to  be 
taken  off  after  the  two  wreath-pieces  are  bolted  together. 


PLATE  13. 

Plate  13.  [Scale,  H^^—1  foot].  Eofhihits  the  cnnstrvction 
of  the  face-mould  for  a  tvrcath-piece,  where  the  cyUndric  sec- 
tion on  i)i(in  is  greater  than  a  quaHer  circJe. 

In  this  case  the  angle  of  tangents  on  plan  will  be  acute. 
Three  kinds  of  face-moulds  are  here  shown.  Classified  thus  :  A 
face-mould  for  a  wreath-piece  containing  a  full  easing  ;  one  with- 
out an  easing,  and  the  other  with  an  intermediate  easing.  We  will 
first  show  how  to  draw  the  face-mould  for  a  Y>'reath-piece  having 
a  full  easement.  > 

Fig.  1.  TJie  shaded  imH  shotvs  the  cylindric  section  on 
plan. 

The  radius  OA,  OC,  for  the  center  line  of  rail  equals  IS^''; 
the  width  of  rail  S  3,  equals  4^^.  At  right  angles  to  the  radii 
OA  and  OC,  draw  the  tangents  AB  and  CB.  From  A,  and 
perpendicular  to  tangent  CB,  draw  A  7.  for  the  seat  of  bevels. 
Draw  the  chord  AC,  also  the  diagonal  BO,  cutting  the  chord  at  J. 

Fig.  2.    Exhibits  the  elevation  of  tangents. 
Let  XX  indicate  a  base  line.     Make  CB  and  BA  equal  tan- 
gents CB  and  BA,  Fig.  1 ;  perpendicular  to  XX,  draw  CD,  BG 


60  Plate  13^ 

and  AL;  assiime  CD  to  be  the  height  that  the  wreath-piece  has 
to  raise  ;  as  the  wreath-piece  has  to  have  a  full  easing,  then  one 
tangent  will  be  horizontal  and  the  other  tangent  will  incline 
the  whole  height. 

Then  draw  BD  for  the  inclination  of  tangent  CJB,  on  plan, 
tangent  AB  \YiIl  be  level.  Make  CH  equal  tlie  diagonal  HO  on 
plan,  Fig.  1 ;  make  CF  equal  the  chord  AC  on  plan,  Fig.  1, 
Make  CE  equal  BJ,  Fig.  1 ;  let  B  7  equal  B  7,  Fig.  1.  From 
7,  and  square  to  BD  draw  7  8.  Bisect  the  height  CD  at  N; 
draw  NE  produced,  to  intersect  the  perpendicular  from  H  at  K, 

Bevels.  Returning  to  plan,  Fig.  1,  make  7  8  equal  7  8, 
Fig.  2,  and  7  D  equal  CD,  Fig.  2.  Join  A  8  and  AD  for  the 
bevels  at  8  and  D. 

Fig.  3.    Exhibits  tlie  face-mould. 

Make  CB  equal  BD,  Fig.  2.  AVith  C  as  a  center,  and  FD, 
Fig,  2,  for  a  radius,  draw  arc  at  A;  again,  with  B  as  a  center, 
and  tangent  AB,  Fig.  1,  for  a  radius,  draw  arc  intersecting  at  A; 
Join  BA.  Perpendicular  to  BA  draw  AE  iudefniite  ;  draw  the 
chord  AC.  Bisect  AC  at  D;  draw  BD  prolonged,  to  iutt-rsect 
AE  at  G.  Join  OC  and  we  have  the  trapezium  ABCO,  on  the 
cutting  plane,  or  plane  of  plank,  that  will  agiee  v>'hen  in  posi- 
tion, with  the  trapezium,  or  qudarilateral  ABCO  on  plan,  Fig.  1. 

Proof.  The  diagonal  BD  and  BO  nuist  agree  with  NE  and 
NK,  Fig.  2.  if  so,  the  angle  of  trapezium  at  B  is  correct. 

From  0,  and  square  to  AE,  draw  OX  equal  to  the  radius 
OA,  Fig.  1.  Then  OA  will  be  the  semi-major  axis,  and  OX 
will  be  the  semi-minor  axis  of  the  elliptic  curve. 

Make  X  2,  X  3,  each  equal  the  half  width  of  rail.  [2'^]. 
Make  joint  at  C  square  to  tangent  B  C,  the  major  axis  gives  the 
joint  at  A.  Join  XCand  X  A;  from  points  2  and  3,  draw  the 
proportional  lines  parallel  to  X  A  and  X  C  to  intersect  the  radial 
lines  at  10,  5  and  9,  8  through  which  to  draw  the  elliptic  curves 
of  face  mould.  Now  center  the  trammel  at  O,  square  to  the  minor 
axis  O  X.  Then  take  the  rod  and  set  from  the  pencil  (o  the 
minor  pin,  the  distance  O  X.  [The  minor  pin  is  now  fastened, 
and  the  major  pin  is  loose.]  Now  place  the  pencil  at  A,  and  drop 
the  pins  in  the  groove,  and  fasten  the  major  pin  at  the  point  O. 
■J'hen  trace  the  curve  for  the  center  line  of  rail  through  the  points 
A  X  C.  For  the  concave  side  of  face  mould,  set  from  pencil  to 
minor  pin,  the  distance  O  2.  Now  place  the  pencil  at  .5  and  drop 
the  pins  in  the  groove,  and  fasten  the  major  pin  at  the  point  O, 
then  trace  the  concave  side  of  face  mould  througli  the  points 
5,  2,  9.* 

For  the  convex  side  of  face  mould,  set  from  the  pencil  to 
minor  pin,  the  distance  O  3,  on  the  minor  axis;  then  place  the 
pencil  at  10  and  drop  the  pins  in  the  groove,  and  fasten  the  major 
pin  at  0.  Now  trace  the  curve  througli  the  points  10,  3,  6,  com- 
pleting the  face-mould.  If  a  trammel  is  not  at  hand,  or  the 
inclination  of  tangents  be  steep,  requiring  a  large  trammel,  then 
draw  the  two  right  angles  at  O,  to  indicate  the  scat  of  trammel, 
and  use  a  rod,  and  find  points  in  the  elliptical  curve  as  shown  at 
figure  12,  plate  5.  In  this  case  the  semi-major  and  semi-minor 
axis  are   given.    The  distance  9  (>,  on  the  rod  equals  the  semi- 

*If  the  elliptical  curve  should  cut  the  .joint  at  C,  making  the  dis- 
tance C  4,  greater  than  O  12,  do  not  conclude  the  work  wrong,  for  this 
is  natural.  The  difference  is  greater  in  face  moulds  over  winders  that 
are  steep,  the  variation  regulates  itself  when  the  wreutii  yiece  is 
worked  off  to  the  plumb  bevels,  showing  the  vertical  sides  of  fail  sec- 
tion at  the  joints  to  be  concave  and  conve.x. 


1'LA.TE   13.  01 

minor  axis  O  2,  and  the  distance  9  7  equals  the  semi-major  axis 
OA,  for  the  concave  side  of  mould.  Now  move  the  rod  at  inter- 
vals, keeping  the  points  6  -and  7.  over  the  right  angles  as  shown, 
and  make  points  at  the  &ad  of  the  rod,  through  which  trace  the 
elliptic  curve,  using  a  pliable  strip. 

Repeat  the  operation  for  the  center  and  convex  curves  of  face- 
mould;  OA  and  OX  arc  the  semi-major  and  minor  axis  for  the 
center  line,  and  O  10  and  O  3,  are  the  semi-major  and  minor  axis 
for  the  convex  curve  of  face-mould.  For  long  and  steep  face- 
moulds,  the  system  of  ordinates  as  before  described,  will  be  found 
the  most  convenient  and  economical. 

At  sections  L  and  N  the  tangents  are  shown  squared  across 
the  joints.  The  dotted  line  indicates  a  gauge  line.  The  bevel  in  the 
angle  at  D,  Fig.  1,  is  applied  at  section  L,  from  the  face  of 
crook,  through  the  intersection  made  by  the  gauge.* 

The  block  pattern  is  applied  square  to  the  line  made  from  the 
bevel.  At  section  N,  the  bevel  found  in  the  angle  at  8,  Fig.  1,  is 
applied  from  the  face  of  crook  through  the  center  of  section;  the 
block  pattern  is  then  applied  at  right  angles  to  the  bevel,  thus 
showing  the  twist  of  wreath-piece  in  the  crook.  The  shaded  parts 
show  the  amount  of  wood  required  at  the  joints  to  saw  out  the 
crook;  at  the  normal  line  3  2,  less  wood  is  required,  as  shown  at 
Fig,  3,  riate  12. 

Fig.  4  shows  the  plan  of  a  cylindric  section  greater  than  a 
quarter  circle.  How  to  construct  the  face-mould  for  a  ivreatli- 
picce  tcithout  an  easing.  The  shaded  pait  shoivs  the  cylindric 
section  on  pUtn. 

Let  OA  and  OC  indicate  the  radii.  With  OA  as  a  radius, 
draw  the  center  line  AXC;  draw  the  tangents  AB  and  CB  per- 
pendicular to  OA  and  OC.  From  A,  and  square  to  tangent  BC, 
iraw  A  7,  for  the  seat  of  bevel.  Draw  the  chord  AC  and  the 
liagoualSO. 

Fig.  5.  Exhibits  the  development  and  elevation  of  tan- 
gents. 

Let  XX  indicate  a  base  line.  Make  CB  and  BA  equal  tan- 
gents CB  and  BA  on  plan,  Fig.  4.  Perpendicular  to  XX,  draw 
CD,  BM  and  AL.  Now  as  this  face-mould  is  for  a  wreath- 
piece  without  an  easing,  consequently  both  tangents  will  have 
the  same  inclination,  and  but  one  bevel  will  be  required  for  both 
joints.  Make  CD  e(iual  the  whole  height  the  wreath-piece  has 
to  raise.  Join  AD.  cutting  BM  at  E.  Make  CF  equal  the 
chord  AC,  Fig.  4,  Let  B  7  equal  B  7,  Fig.  4 ;  from  7,  and  per- 
poixdicular  to  AD,  draw  7  G. 

Bevels.  Returning  to  Fig,  4,  make  7  D  equal  FG,  Fig.  .5. 
Join  DA,  and  in  the  angle  at  D  is  found  the  bevel  for  both 
joints. 

Fig.  6.    Exliihits  the  face-mould. 

Make  CB  equal  DE,  Fig,  r,.  With  C  as  a  center,  and  FD 
Fig,  .5,  for  a  radius,  draw  arc  at  A;  again,  with  B  as  a  center, 
and  AG,  Fig.  5,  for  a  radius,  draw  arc  intersecting  at  A.  Join 
BA,  Draw  the  chord  AC.  Bisect  AC  at  D.  Draw  the  diagonal 
BD  prolonged,  to  equal  BO  on  the  plan.  Fig.  4,  as  at  O. 

*The  correctness  of  bevels  may  be  proved  thus,  with  C  as  a  center 
and  the  hypothenuse  of  bevel  as  AD,  Fig.  1,  for  a  radius,  tlic  curve 
must  tangent  AD,  as  shown  at  IJ.  For  the  other  bevel,  AJ  must  equal 
A  8,  Fig.  1. 


63  Plate  13. 

Draw  thp  radial  linos  AO  and  CO  and  we  have  tlic  trapezium 
OABC  on  the  cutting  plane,  that  will  agree  when  in  position, 
with  the  trapezium  OABC  on  plan,  Fig.  4. 

Proof.  The  diagonal  BD  must  equal  BP  on  plan,  Fig,  4. 
As  both  tangents  have  the  same  inclination,  and  are  both  the 
same  length,  then  the  diagonal  OB  becomes  the  director.  Make 
OX  equal  OX,  Fig.  4  for  the  semi-minor  axis  ;  make  X  2  and  X 
3  each  equal  the  half  width  of  rail  [2^^].  Join  XC  and  XA. 
From  2  and  3  draw  the  proportional  lines  parallel  to  XA  and 
XC,  cutting  the  radial  lines  OA  and  OC  at  1  6  and  6  9,  for  the 
points  through  which  the  elliptic  curve  will  pass.  Make  joints 
at  A  and  C  at  right  angles  to  the  tangents  BA  and  BC. 

Now  pivot  the  trammel  at  O  with  the  axis  at  right  angles  to 
the  minor  axis  OX;  then  set  the  minor  pin  from  pencil  to  equal 
O  2  for  the  concave  side  of  face-mould.  Now  place  the  pencil  in 
the  point  at  6,  and  drop  the  pins  In  the  grooves,  and  fasten  the 
major  pin  ;  then  trace  the  curve  through  the  points  6  2,  G  for  tlio 
concave  side  of  face-mould.  For  the  center  line,  set  from  pencil 
to  minor  pin  the  distance  OX;  place  the  pencil  in  the  point  at  C 
and  drop  the  minor  pin  in  the  groove,  then  slide  the  major  pin 
until  it  drops  into  the  groove,  then  fasten  the  pin  and  trace  the 
center  line  of  face-mould. 

For  the  convex  side,  set  from  pencil  to  minor  pin  the  distance 
O  3  on  the  minor  axis;  then  place  the  pencil  in  the  point  at  9,  and 
(h-op  tlio  pins  into  the  grooves ;  then  fasten  the  major  pin  and 
trace  the  convex  curve  of  face-mould  through  the  points  1,  3,  9. 
Sections  L  and  iVshow  the  bevel  found  in  the  angle  at  D,  Fig. 
4,  ai)plied  througli  the  center  of  joints.  The  l)lock  pattern  is 
applied  square  to  tlie  Ijevel,  and  shows  the  twist  of  wreath-piece 
at  tlie  joints.  For  all  wreath-pieces  greater  than  a  quarter  circle, 
a  bevel  will  I)e  required  at  both  joints,  and  they  will  always  cross 
the  tangents,  because  there  will  always  be  a  point  in  the  face- 
inoiild  lliat  will  be  equal  to  the  true  v.'idthof  rail,  which  is  termed 
the  normal  line. 

Fig.  7.  Exh'ihits  ihe  (jround  plan  of  d  cyllndrie  section 
greater  Uian  a  quarter  circle.  How  to  construct  the  face-mould 
for  a  wrcath-piccc,  liaving  an  intermediate  easing. 

Witli  OA  for  a  radius,  draw  the  center  line  of  rail  AXC, 
The  shaded  part  shows  the  true  width  of  rail  on  plan.  Perpen- 
dicular to  tlie  radii  OA  and  OC,  draw  the  tangents  AB  and  CB. 
Draw  tiie  cliord  ACaiul  the  diagonal  BO,  cutting  the  chord  at  P. 
From  A,  and  square  to  tangent  BC,  draw  A  7. 

Fig.  8  shows  the  development  and  elevation  of  iangent  from 
plan  Fig.  7. 

Let  XX  indicate  a  base  line.  Make  CB  and  BA  equal  the 
tangents  CB  and  BA,  Fig.  7;  perpendicular  to  XX,  draw  CD, 
BM  and  AL,  indefinite.  Now  for  a  wreath-piece  having  an 
int«'riiiediate  casing,  both  tangents  must  be  inclininir,  but  one  must 
have  a  greater  inclination  than  the  other.  Let  BG  be  the  height 
that  tlu!  lower  tangent  has  to  raise,  and  CD  the  wliole  height  of 
both  tangents.  ,Toin  AG  ami  GD  for  the  increased  length  of 
tangents  in  elevation;  prolong  tangent  AG,  to  cut,  tlje  perpendic- 
ular CD  at  E;  also  prolong  tani^ent  DG  to  intersect  the  liase 
line  XX  n[,  H.  Make  CF  equal  AC,  Fig.  7.  Let  CP  and  CJ 
equal  SP*  and  BO  on  plan.  Fig.  7;  also  make  B  7  and  ilfiVeach 
equal  B  7  on  plan,  Fig.  7.  From  7  and  square  to  HD.  draw  7  8, 
and  I'rom  N  and  square  to  AE,  draw  N  9.  Bisect  ED  at  R. 
Make  CS  equal  ER.  From  /S  through  P  draw  a  line  to  intersect 
the  perpendicular  from  J  at  K, 


Plate  13.  63 

Bevels.  As  both  tangents  in  this  case  have  different  incli- 
nations, two  bevels  will  be  required. 

Return  to  plan,  Fig.  7,  and  prolong  tangent  CB  indefinite. 
Make  7  8  equal  7  8  in  elevation,  Fig  8;  also  make  7  9  equal  iV9 
iu  elevation,  Fig.  8.  Join  8  A  and  9  A  for  tlie  bevels  required, 
as  shown  in  the  angles  at  8  and  9  on  plan.  Fig.  7. 

Fig.  9.    Exhibits  the  face-mould. 

Make  CBN  equal  DGH,  Fig.  S;  then  with  C  as  a  center 
and  DF,  Fig.  8,  lor  a  radius,  draw  arc  at  A;  again,  with  B  as  a 
center,  and  tangent  AG,  for  a  radius,  draw  arc  intersecting  at  A, 
join  JBA,  draw  the  chord  AC;  bisect  AC  at  D:  draw  BD 
indefinite. 

Proof.  If  the  diagonal  BD  equal  PS,  Fig.  8,  then  the  angle 
of  tangents  is  correct.  Make  BO  equal  KS,  Fig.  8;  draw  the 
radial  lines  OA  and  OC,  indefinite  ;  join  AN  for  the  director; 
from  the  center  O,  draw  OX,  indefinite,  and  parallel  to  director 
AN.  Make  OX  equal  the  radius  OA,  Fig.  7.  for  the  semi-minor 
axis;  througli  O,  and  at  right  angles  to  OX,  draw  0  6  for  the 
direction  of  the  major  axis. 

''  Make  joints  at  A  and  C  perpendicular  to  the  tangents  AB 
and  CB:  nuike  X  2  and  X  o  each  equal  the  true  width  of  rail. 
Connect  XA  and  XC.  From  2  and  3  draw  the  inoportional 
lines  parallel  to  XA  and  XC  to  intersect  OA  and  OC  prolonged, 
at  7  7  and  8  8,  for  the  correct  points  through  which  the  elliptic 
cui've  will  pass. 

The  points  8  8  and  7  7  on  the  radial  lines,  are  the  points  of 
tangeney,  or  the  connecting  points  of  the  straight  with  the  circu- 
lar part. 

To  trace  the  face  mould  with  a  trammel,  pivot  the  trammel 
in  O,  with  the  arms  resting  on  G  0.  For  the  convex  side  of 
mould;  set  from  pencil  to  minor-pin  the  distance  O  3,  then  place 
the  pencil  in  tlie  point  at  8,  drop  the  minor-pin  in  tlie  groove  at 
0,  and  slide  the  major-pin  until  it  drops  in  tlie  groove  at  9,  then 
fasten  the  major-pin,  and  trace  the  elliptic  curve  through  the  points 
7,  3,  8;  repeat  the  operation  for  the  center  and  concave  side  of 
face- mould. 

If  room  be  a  consideration  then  use  the  ordinates  for  any  of 
of  these  moulds,  by  drawing  the  ordinates  parallel  to  the  director 
AN,  using  tlie  chords  as  base  lines  as  directed  in  former  plates. 
At  sections  L  and  N  the  tangents  are  shown  squared  across  the 
joints,  and  the  plank  is  centered  as  indicated,  by  the  dotted  gauge 
lines,  and  the  bevel  found  in  the  angle  at  9,  Fig.  7,  is  applied  at 
the  joint  A,  and  the  bevel  found  in  the  angle  at  8,  Fig.  7,  is 
applied  at  joint  C,  Tlie  block  pattern  is  then  applied  at  right 
angles  to  the  lines  made  from  the  bevels  and  gives  the  twist  of 
wreath-piece  at  the  joints  as  shown.  Observe  tiie  bevels  as  ajiplied; 
cross  the  tangents,  because  the  minor  axis,  O  3,  is  in  the  mould. 
At  the  points  3  and  3,  the  bevels  blend  and  the  section  of  rail  at 
that  jioint  is  siiuare  to  tlie  face  of  crook.  The  sliding  of  the 
mould  has  been  explained  and  applies  the  .same  here. 

Observe  the  bevel  at  section  L  is  applied,  so  as  to  throw  the 
joint  at  Cup,  and  tiie  bevel  at  section  JVis  applied  so  as  to  throw 
the  joint  at  A  down,  corresponding  to  the  ta.ngeuts  AG  and  GD 
\n  elevation. 


6^  Plate  14. 


PLATE   14. 

Plate  14.  [Scale,  M^^=l  footj.  Ea:hibits  the  constructicni 
of  a  fcwc-inoald  for  a  wreuthr-piece  over  a  cylindric  section,  that 
is  elliptic  071  plan,  said  section  being  less  than  a  quarter  of  an 
ellipse. 

Figs.  1,  2  and  3.  SJimi'showto  constructthefacc-^nonld 
for  a  wrcath-yiccc  vnthmit  an  casitKj. 

The  plan  of  the  twist  part  of  rail  being  less  than  a  quarter  of 
an  ellipse.  Draw  the  center  line  ASB  of  the  ellipse,  also  draw 
joints  at  A  and  B  normal  to  (he  curve.*  At  right  angles  to  the 
joints,  draw  the  tangents  AC  and  BC;  parallel  to  AC  and  BC 
draw  AO  and  BO  for  the  ))arallelograni  OACB  on  plan.  Par- 
allel to  the  center  line  ASB  set  off  the  width  of  rail,  draw  the 
chord  AB;  prolong  tangent  BC  indefinite,  from  A  and  square  to 
.BC  draw  AD 

Fig.  2.  Exhibits  the  development  and  elevation  of  tan- 
gents from,  plan,  Fig.  1. 

Let  XX  indicate  a  base  line.  Make  BC  and  CA  eriual  tan- 
gents BC  and  CA  on  plan,  Fig.  1 ;  perpendicular  to  XX  draw 
BD  and  C^  indefinite.  Assume  BD  to  be  the  whole  height  the 
wreath-piece  has  to  raise,  connect  AD,  cutting  CE  at  H,  for  the 
inclination  of  tangents. 

Make  CJ"  e(|ual  CD,  Fig.  1;  make  DG  c(iual  twice  CH; 
let  BJ' equal  OC,  Fig.  1,  make  SiT  equal  the  chord  BA,  Fig,  1; 
from  J,  and  perpendicular  to  AD,  draw  JL. 

Bevels.  As  both  tangents  have  the  same  inclination,  only 
one  bevel  will  be  reijuired.  IJeturn  to  Fig.  1,  make  DNi:nna\  J 
L,  Fig.  '.i,  join  NA  for  the  bevel  at  N.  Parallel  to  .BiV  draw  the 
half  width  of  rail  to  cut  the  hypothenuse  NA  at  Q 

Fig.  3.     Exhibits  the  face-mould. 

Make  BC  eiiiial  DH,  Fig.  ;3;  with  B  as  a  center  and  DK, 
Fig.  2,  for  a  radius,  draw  arc  at  A;  again,  with  C  as  a  center, 
and  tangent  AH\n  elevation.  Fig.  2,  for  a  radius,  draw  arc  inter- 
secting at  A;  join  CA.  Paralh;!  to  AC  and  BC,  draw  BO  and 
AO  for  the  parallelogram  OACB,  on  the  cutting  phuie,  that  when 
in  position  will  agree  with  the  parallelogram  OACB,  on  plan. 
Fig.  1. 

Proof.  The  diagonal  CO,  must  ecjual  the  distance  FG,  Fig. 
2.  If  so,  the  angle  of  tangents  at  C,  must  be  correct.  Draw  tlie 
chord  AB,  bisect  AB  at  D;  bisect  BD  and  AD  at  ^  and  J'. 
Make  BH  equal  AH,  Fig.  2;  join  HO  for  the  director.  From 
the  points  A,  E,  D,  F  and  B,  on  the  chord  line,  draw  ordinates 
indefinite  and  parallel  to  HO. 

Ileturu  to  plan,  Fig.  1;  bisect  the  chord  AB  at  J;  bisect  AcT 
and  BJ  at  E  and  F:  make  SiJ equal  CA  in  elevation.  Fig.  2, 
connect  HO  tor  the  director  on  plan.  From  the  points  A,  E,  J, 
JF*  and  B,  draw  ordinates  paralhil  to  the  director  iifO  to  cut  the 
concave,  center  and  convex  curves  at  2,  S  and  4.  Iteturning  to 
Fig.  3. 

Make  joints  at  A  and  B  at  right  angles  to  the  tangents  AC 
and  BC.    Let  A  5  and  A  0,  also  B  7  and  B  8,  each  e(iual  NQ, 


*To  draw  a  lino  normal  to  the  elliptic  curve  at  any  point  in  the 
curve,  sec  Fig.  8,  Phitc  5. 


Tr-ATK  14.  Co 

Fig.  1.  Now  transfer  tlie  points  2,  3  and  4,  from  the  orilinateson 
plan,  Fig.  1,  to  corresponding  ordinates  on  face-monld  :  then 
trace  the  concave  side  of  face  mould  tlirough  the  points  7,  ;3,  5; 
and  the  convex  side  through  the  points  8,  4,  G,  using  a  pliable 
strip. 

The  sections  at  P  and  It  show  the  tangents  carried  across  the 
joints  square  to  the  face  of  crook;  the  joint  is  centered  witli  the 
gauge  and  tlie  bevel  found  in  the  angle  at  N,  Fig.  1.  is  shown 
applied  through  the  center  of  both  sections  so  as  to  pitch  the 
joint  at  A  down,  and  the  joint  at  R,  up. 

The  block  pattern  is  then  applied  square  to  the  line  made 
from  the  bevel,  showing  the  twist  of  rail  section  at  the  joints;  the 
shaded  part  shows  the  width  required  at  the  joints  to  saw  out  the 
crook  in  the  rough,  and  also  tbe  amount  of  surplus  wood  to  be 
removed  in  squaring  up  the  wreath-piece. 

Fig's.  4,  5  and  6.  Exhibits  the  construction  of  face- 
mould  ivhen  the  ivrcatJi -piece  has  an  intermediate  casing,  Vac  jAan 
being  Vie  same  as  at  Fig.  1. 

Fig  4.    Shows  the  plan. 

The  joints  at  A  and  B  are  drawn  normal  to  the  center  elliptic 
curve  ASB;  and  the  tangents  AC  and  BC are  at  riglit  angles  to 
the  joints.  Draw  AO  and  BO  parallel  to  tangents  AC  and  BC: 
from  B  and  at  right  angles  to  tangent  AC  prolonged,  draw  BT; 
from  A,  and  perpendicular  to  tangent  .BC prolonged,  draw  AV, 
connect  AB  f(Jv  the  chord.  Bisect  AB  at  D;  bisect  AD  and  B 
n  at  E  and  F;  bisect  AE  at  H. 

Fig.  5.  Shows  the  developmcni  and  elevation  of  tangents 
from  the  plan,  Fig.  4. 

Let  XX  be  a  base  line;  make  .BC  and  CA  equal  tangents 
JBCand  CA,  Fig.  4.     Perpendicular  to  XX,  draw  BD  and  CE. 

As  the  wreath-piece  is  to  contain  an  intermediate  easing,  the 
tangents  will  liave  dilferent  inclinations.  We  will  assume  Cffto 
))e  the  height  that  the  tangent  AC  on  plan  has  to  raise,  and  BD 
as  the  lieight  that  both  tangents  are  required  to  raise. 

Draw  tangent  DH,  prolonged  to  intersect  XX  at  J;  draw  the 
tangent  Aiifprolonged.  JIake  CV  equal  CV,  Fig.  4;  also  make 
^r equal  CTon  plan.  fig.  4:  from  Vand  square  to  tangent  DH 
prolonged,  draw  VK;  from  Tand  at  right  angles  to  tangent  Ai? 
prolonged,  draw  TM, 

Make  BQ  equal  tlio  diasonal  CO  on  plan.  Fig.  4;  let  BS 
equal  the  chord  AS,  Fig.  4;  nu\ke  DJV  equal  twice  the  height  .ffC 

Bevels.  As  both  tangents  have  different  inclinations  two 
bevels  will  be  required.  Make  VB,  ¥iz.  4,  equal  VK,  in  eleva- 
tion, Fig.  V).  Join  BA;  parallel  witli  BB  draw  the  half  width 
of  rail  [2^^]  to  cut  the  hypothenuse  of  bevel  at  5.  The  angle  at 
P  gives  the  bevel  as  shown.  For  the  other  bevel,  make  BR, 
Fig.  .5,  equal  S27,  Fig.  4;  let  BZ7 equal  TM;  join  UR,  and  the 
angle  at  17"  gives  the  bevel.  I'arallel  to  BD  draw  the  half  width 
of  rail  [2^^]  to  cut  the  hypothenuse  of  bevel  at  G. 

Fig.  6.    Exhibits  the  face-mould. 

Make  BC  equal  tangent  DH  in  elevation.  Fig.  5.  With  B 
as  a  center,  and  DS,  Fig.  .5,  for  a  radius,  draw  arc  at  A;  again, 
with  C  as  a  center,  ami  tangent  AH,  Fig.  5,  for  a  radius,  draw 
arc  intersecting  at  A;  join  CA;  parallel  to  tangent  AC  and  BC 
draw  BO  and  AO.  establishing  the  parallelogram  OACB  on  the 
cutting  plane,  tiiat  will,  Vvhen  in  position,  agree  with  the  parallel- 
ogram OACB  on  plan,  Fig.  4. 


66  Plate  14. 

Proof.  The  diagonal  OC  must  equal  the  distanre  QN,  Fijr. 
5.  Draw  the  chord  AB.  Bisect  AB  at  JD;  bisect  AD  and  BD 
at  E  and  J^'  bisect  AE  at  ^,  Make  BL  equal  JiT,  Fig.  .O; 
join  LO  for  the  director  on  tlie  face -mould.  From  the  points  A, 
H,  E,  D,  i^^and  B  draw  ordinates  indefinite  and  parallel  to  the 
director  LO, 

Malie  joints  at  A  and  B  square  to  the  tangents  AC  and  BC; 
let  A  0  and  A  7  each  equal  Z70,  Fig.  5;  make  B  5  and  B  8  eacli 
equal  P  5,  Fig.  4.  Now  transfer  tiie  points  2,  3  and  4  from  tlie 
ordinates  on  plan,  Fig.  4,  to  corresponding  ordinates  on  the  face- 
mould  as  shown,  using  the  chords  for  base  lines;  at  section  M 
tlie  bevel  found  in  the  angle  at  Z7,  Fig.  .5,  is  applied,  and  at  sec- 
tion N,  the  bevel  found  in  the  angle  at  P,  Fig.  4,  is  applied  in  the 
usual  way. 

Observe  the  bevels  cross  the  tangents  because  there  is  a 
point  in  the  mould  that  is  narrower  than  at  either  of  the  joints. 

Figs.  7,  8  and  9.  Are  introduced  to  hIiow  a  faee-mo^ild 
having  both  tangents  inclinimj,  and  at  the  same  time,  the  bevels 
will  not  cross  the  tangents. 

This  never  happens  only  when  the  eylindric  section  on  plan 
is  less  than  a  quarter  circle,  or  a  quarter  of  an  ellipsis,  tor  then 
the  angle  of  tangents  is  obtuse;  there  are  five  different  face- 
moulds  for  the  obtuse  plan  as  follows  : 

FiEST.  A  face-mould  having  one  tangent  level,  the  other 
inclining,  requiring  two  bevels,  that  in  no  case  cross  the  tan- 
gents in  their  application,  such  as  the  ordinary  newel  wreath,  or 
for  startings  and  landings  where  one  of  the  tangents  is  horizontal, 
as  shown  at  Fig.  3,  Plate  10. 

Second.  When  both  tangents  are  inclining  and  different  in 
their  inclination,  requiring  two  bevels,  which  in  tlieir  application, 
do  not  cross  the  tangents,  as  at  Fig.  9. 

•,  TiiiKD,  When  both  tangents  are  inclining  and  different  in 
their  inclination,  but  requiring  only  one  bevel,  the  square  being 
applied  at  the  opposite  joint,  as  at  Fig.  12. 

FouKxn,  When  both  tangents  are  inclining  and  different  in 
their  inclination,  requiring  two  bevels,  but  crossing  the  tangents, 
as  shown  at  Fig.  6. 

Fifth,  Having  both  tangents  inclining  and  of  the  same  in- 
clination, requiring  only  one  bevel  for  both  joints,  and  crossing 
the  tangents  in  their  application,  as  shown  at  Fig,  3. 

Fig.  7.    Sliows  the  plan  of  tangents  and  repeats  Fig.  1. 

Tlie  joints  at  A  and  B  are  draAvn  nonnal  to  the  curve;  the 
tangents  AC  and  SC  are  drawn  square  to  the  joints;  AO  and  BO 
are  parallel  to  jBCand  AC,  creating  the  parallelogram  AOCB  on 
plan.  From  A  and  at  right  angles  to  tangent  SCprolonged,  draw 
AD;  from  B  and  square  to  tangent  ACprolongeil,  draw  BE. 

Pig.  8.  Exhibits  the  development  and  elevation  of  tangents^ 
Let  XX  indicate  a  base  line;  make  BC  and  CA  equal  the 
tangents  BC  and  CA,  Fig.  7.  At  right  angles  to  XX.  draw  the 
perpendiculars  BD  and  CF,  indefinite;  assume  CHio  be  the  height 
for  the  lower  tangent  and  BD,  the  height  for  both  tangents;  draw 
the  tangent  AH,  prolonged  indefinite;  draw  the  tangent  DH 
prolonged  to  intersect  the  base  line  XX  at  3.  Make  CJ"  equal 
CD  on  plan,  Fig.  7;  make  EG  equal  CJ'on  plan.  Fig.  7;  h^XBK 
equal  the  chord  AB  on  plan,  Fig.  7,  and  BL  equal  the  diagonal 
CO  on  plan,  Fig.  7.     Make  DM  equal  twice  the  hight  of  CH, 


Platk  14.  67 

join  LM  for  the  length  of  diagonal  on  the  face-mould,  connect 
DK  for  the  length  of  chord  on  the  face-mould.  From  J  and 
s(iiiare  to  tangent  DH  prolonged,  draw  JN;  also  from  G  and 
square  to  tangent  A Jif  prolonged,  draw  GP. 

Keturn  to  plan,  Fig.  7,  make  BL  equal  C2  in  elevation  Fig. 
8,  connect  LO  for  the  liirector  on  plan.  Bisect  the  chord  AB  at 
Q;  bisect  AQ  and  BQ  at  R  and  S;  bisect  AR  at  T. 

From  the  points  A,  T,  R,  Q,  S,  and  B,  draw  ordiuates  paral- 
lel to  the  director  OL,  to  cut  tlie  concave,  center  and  convex  curves 
of  rail  at  3,  .3  and  4. 

Bevels.  Make  DH  on  plan,  Fig.  7,  equal  JN  in  elevation 
Fig.  8;  join  AiJ  for  the  hypothenuse  of  bevel.  Make  i^J"  equal 
GP,  Fig.  S;  join  JB  for  the  hypothenuse  of  bevel  at  the  wide  end 
of  mould. 

Parallel  to  tangent  CB,  draw  the  half  width  of  rail  [2'']  to 
cut  HA  at  5;  parallel  to  tangent  AC,  draw  the  half  width  of  rail 
to  cut  JB  at  7. 

Fig.  9.     Erhihits  the  facc-moidd. 

Make  SC  equal  tangent  DH  in  elevation  Fig.  8;  with  Sasa 
center  and  DK,  Fig.  8,  for  a  radius,  draw  arc  at  A;  again,  with 
C  as  a  center  and  tangent  AH,  for  a  radius,  draw  arc  intersecting 
at  A;  join  CA,  parallel  to  AC  and  BC,  draw  BO  and  AO  for  the 
parallelogram  OACB  on  tlie  cutting  plane,  or  plane  of  plank 
tiiat  will  agree  when  elevated  into  position  with  the  parallelogram 
OACB  on  plan,  Fig.  7. 

Proof.  The  diagonal  DC  must  agree  with  the  length  of  LM, 
Fig.  8.     If  so,  the  angle  of  tangents  at  C  is  correct. 

Make  BD  equal  ^"2,  Fig.  8,  connect  DO  for  the  director  on 
the  face-mould;  draw  the  chord  AB.  Bisect  AB  at  Q;  bisect 
AQ  and  BQ  at  R  and  S;  Insect  AR  at  T.  From  tlie  points  A. 
T,  R.  Q,  S  and  B,  draw  ordinates  indefinite;  make  joints  at  A 
and  B  square  to  the  tangents  AC  and  BC;  let  A  7  and  A  8  each 
equal  J  7,  Fig.  7;  also  make  B  5  and  B  6  each  ecpial  H  5,  Fig.  8. 
Now  transfer  points  2,  ."  and  4  from  the  ordinates  on  plan,  Fig.  7, 
to  corresponding  ordinates  on  the  face-mould  as  shown;  then  trace 
the  curve  through  the  points  8,  4,  6,  for  the  convex  side,  and 
through  the  points  7,  2,  5,  for  the  concave  side  of  face-mould. 

The  sections  at  M  and  .ZV  show  the  bevels  applied  in  the  usual 
way;  observe  they  do  not  cross  the  tangents,  because  the  long 
tangent  DH,  in  elevation,  intersects  the  horizontal  line  XX, 
between  tlie  point  J"  and  the  center  perpendicular  from  C.  This 
will  be  explained  at  Fig.  11. 

Pig's.  10,  11  and  12.  Exhibit)^  a  plan  of  tanrjcnts  tluit 
rcpatts  Fig.  1.  To  show  the  crmstruction  of  a  face-mould  on  the 
(UvkUnfj  line  hclwecn  one  in  which  the  bevels  cross  the  tangents 
■bi  their  application,  and  a  faee-moiild  in  lolvicli  the  bevels  do  not 
cross  the  ianfjenls. 

Fig.  10.    Shows  the  plan. 

The  joints  A  and  JB  are  made  normal  to  the  curve,  and  the 
tangents  AC  and  BC  are  drawn  at  right  angles  to  the  joints; 
iiarallel  to  AC  and  BC  draw  BO  and  AO  for  the  parallelogram 
OACB.  At  right  angles  to  tangent  BC  prolonged,  draw  AD; 
also  from  B  and  at  right  angles  to  tansent  AC  prolonged, 
drav/  BF. 

Fig.  11.     Shoics  the  development  arul  elevation  of  tangents. 

Let  XX  indicate  a  base  line;  make  BC  and  CA  equal  the 

tangents  BC  and  CA,  Fig.  10.     From  XX  erect  the  perpendic- 


68  i^LATE   14. 

ulars  BD  ami  CD;  assume  CF  to  be  the  height  that  tangent  AC 
oil  plan  is  required  to  raise;  make  CJ  equal  CD,  Fig.  10.  Con- 
nect JF,  and  prolonged  to  intersect  the  perpendicular  SD  at  D; 
then  BD  is  the  whole  height  of  wreath-piece,  from  center  to  cen- 
ter of  rail,  and  A^and  FD  are  the  increased  length  of  tangents 
AC  and  BC  on  plan  Fig.  10.  At  right  angles  to  BD  draw  DE; 
make  EH  equal  CF,  Fig.  10;  from  H,  and  at  right  angles  to 
AF,  prolonged,  draw  HK;  make  BL  equal  the  diagonal  OC. 
Fig.  10;  make  BM  equal  the  chord  .BA  on  plan,  Fig.  10;  let  DN 
equal  twice  FC. 

Return  to  plan,  Fig.  10.  In  this  case  DA  becomes  the 
dii'ector  on  plan;  draw  the  chord  AB.  Bisect  AB  at  Q;  bisect 
AQ  and  BQ  at  R  and  S;  bisect  AR  at  T;  from  the  points  T, 
R,  Q  and  /S,  draw  ordinates  parallel  to  the  director  AD,  to  inter- 
sect the  coucave,  center  and  convex  curves  of  rail  at  2,  3  and  4. 

In  this  case  only  one  Ijevel  will  be  required,  because  the  tan- 
gent DF  in  elevation,  Fig.  11,  when  prolonged,  intersects  tiie 
base  line  XX,  at  the  point  J,  and  the  point  J  coincides  with  the 
point  D,  Fig.  10,  whieli  is  square  from  the  point  A  to  the  tangent 
BC,  Fig.  10;  and  DA  then  becomes  the  director,  and  is  parallel 
in  this  case  with  the  joint  at  B. 

Observe  in  elevation,  Fig.  11,  when  the  tangent  DJ*  is  pro- 
longed to  the  bas(!  line  XX;  if  it  intersects  the  base  line  between 
the  points  J"  and  C,  as  siiown  at  C2,  Fig.  S,  in  all  such  cases,  two 
bevels  will  be  re(juired,  ))ut  they  will  not  cross  the  tangents  in  their 
application.  But  if  the  inclination  of  tangent  Z)i^  should  inter- 
sect the  base  line  to  the  left  of  the  point  J,  then  there  will  be  two 
bevels  required,  and  also  they  will  always  cross  the  tangents  as 
shown  at  Fig.  5,  where  tangent  DH  produced  intersects  the  base 
line  XX  at  J  to  the  left  of  the  jioint  V.  Let  it  be  rememl^ered 
from  this  that  the  i>oint  J,  is  the  dividing  point  in  the  application 
of  the  bevels,  as  to  eitlier,  they  cross  the  tangent,  or  tliey  do  not. 

Let  the  student  bear  tliis  in  mind,  for  it  is  ditficult  sometimes 
to  know  which  way  to  apply  the  bevels;  this  only  liappens  when 
the  tangents  on  plan  are  obtuse  at  tlie  anglt;  C;  when  the  tangents 
on  ]ilan  are  acute,  bear  iu  mind  that  the  bevels  will  always  cross  the 
tangents  iu  their  application. 

Wbcn  the  tangents  on  plan  form  arifcht  anjile,  the  bevels  will  cross 
llic  tiuisents  on  all  wrealli-pieces  where  boMi  tiuiLreuts  are  inclining, 
and  wlioro  one  tangent  is  level,  and  the  otlier  inclining,  the  square 
will  apply  to  tlie  joint  made  on  the  inclining  tangent. 

Bevel.  Prolong  BO,  Fig.  10  indefinite;  make  BM  equal 
HK  \n  elevation.  Fin.  11;  join  i^ikf  for  the  bevel  at  M;  parallel 
witl\  SikTdraw  the  half  v,'idlh  of  rail  [2^^]  to  cut  MF  at  9. 

Pig.  12.    Exlilhiis  tli-e  face-mould. 

Make  BC  equal  DF,  Fig.  11;  with  B  as  a  center,  and  the 
distance  DM,  Fig.  11,  for  a  radius,  draw  arc  at  A;  again  with  C 
as  a  center,  and  tangent  AF,  Fig.  11,  for  a  radius,  draw  arc  inter- 
spcting  at  A.  Connect  AC;  parallel  to  ACaud  BC,  drawiJO  and 
AO,  creating  the  parallelogram  OACB  on  the  cutting  plane,  that 
will  coincide  with  the  parallelogram  OACjBoii  plan  when  elevated 
into  position.  iVLike  joints  at  A  and  B  perpendicular  to  tiie  tan- 
gents AC  and  BC;  draw  the  cliord  AB.  Bisect  AB  at  Q; 
Insect  AQ  and  BQ  at  R  and  S;  bisect  Ai2  at  T.  Make  JBZ) 
equal  JF  in  elevnlion.  Fig.  11;  join  DO;  tlien  DO  becomes  th(! 
director,  wliich  is  at  right  angles  to  tangent  BC.  From  the  points 
A,  T,  R,  Q  and  S,  draw  ordinates  indefinite  and  parallel  to  the 
director,  then  transfer  the  points  2,  3  and  4  on  the  ordinates  on 
plan,  Fig.  10,  to  corresponding  ordinates  on  face-mould  as  shown. 


Plate  15.  69 

Make  JB  7  and  B  S  each  equal  B  7  and  B  8  on  plan.  Fig.  10; 
let  A  5  and  A  6  each  equal  Md,  Fig.  10;  now  through  the  points 
5,  3,  7  trace  the  concave  curve,  and  through  tlio  points  G,  4,  8 
trace  the  curve  for  tlie  convex  side  of  face  moiikl. 

The  section  at  N  shows  the  bevel  found  in  tlie  angle  at  M, 
Fig.  10,  applied  in  the  usual  waj';  at  section  M  tlie  siiuare  is 
applied  fiom  the  face  of  erode  as  sliown. 

If  it  be  required  to  find  the  point  of  tangency,  prolong  DA, 
Fig.  10.  With  T  as  a  center,  and  TA,  Fig.  12,  for  a  radius, 
intersect  DA  at  K;  draw  TK  ])volonged,  draw  G  P  parallel  to 
DK.  Make  AP,  Fig,  12,  equal  KF,  Fig.  10;  draw  JPL  parallel 
to  OD  and  equal  to  L  G,  Fig.  10;  draw  LA  prolonged,  make  AV 
equal  AL,  then  Z»  and  V  are  the  points  of  tangency. 


PLATE  15. 


Plate  15.  [Scale  M^'' — l  foot.]  Shows  how  to  place  the 
rUsers  cuid  buhisters  in  jiUttform  (uid  quarter-pace  c]]U)idcrii. 
When  winders  in  a  semi-circle  are  to  l>c  used,  Fi'fa.  15  aud  la 
shows  hoiv  tlie  treads  tnuy  he  (jradnatedin  ivldthattlie  iKf/Twr 
ends  so  as  to  forma,  graceful  curve  connectinfjtheivrcath  part  of 
string. 

Fig.  1.     Shoxvs  a  C -cylinder. 

The  tread  is  to  be  9^^;  the  radius  Oi^ecnials  .3^^;  with  0  for  a 
center  and  OF  [:/']  for  a  radius,  draw  tlie  semi-circle  BFC; 
draw  BA  and  CD  to  indicate  tlie  straight  part  of  outer  string 
connecting  the  circidar  part.  Witli  J*  as  a  center  and  FO  for  a 
radius,  draw  arc  intersecting  at  H;  tlirough  i^'and  iifdraw  a  line 
to  intersect  DC  prolonged,  and  also  CB  prolonged,  at  J'aufl  K; 
then  iTis  the  focus  and  the  distance  JC  is  the  stretchout  of  the 
curve  from  JPto  C,  Now  make  from  J"  to  the  face  of  No.  16  j-ise 
to  equal  half  a  tread  Vi''\  and  from  face  of  No.  IG  to  face  of 
No.  17  rise,  to  equal  'J^^;  opposite  Nos.  IG  and  17  rise,  draw  the 
face  of  No.  15  and  14  rise,  thus  locating  the  face  of  risers  iu  a  iV 
cylinder. 

Observe  the  face  of  Nos.  14  ;ind  17  rise  are  8I/3"  fi-orn  the  .iointof 
cylinder  on  the  striii;-;ht  i)art  of  strinjr;  tliis  must  be  carefully  noled 
when  proceeding  to  construct  tl\e  face-mould,  so  that  the  correct 
height  of  wrouth-pieco  Lua,y  be  established. 

Fig's.  2  to  4.     Shoivs  o.  7^^,  8^^  and  f/^  cijllndcr. 

The  location  of  risers  are  found  in  the  sanii?  manner  as  at  Fig, 
1,  the  lettering  being  the  same.  Oljserve  at  Fig.  2  tlie  face  of  No. 
12  and  15  rise  are  opposite  and  equal  8''^  from  the  spring  of  cylin- 
der; at  Fig.  3  the  face  of  risers  is  714^^  from  the  s])ring  of  cylin- 
der ;  at  Fig.  4  the  tread  is  10^^,  and  the  face  of  Nos.  i:j  and  10 
risers  is  8^^  from  the  joint  of  cylinder. 

Fig.  5.     Shows  a  cylinder  10^^  in  diameter. 

The  stretchout  CJ" for  the  (luailer circle  and  location  of  liscrs, 
repeats  Fig.  1,  tlie  treads  are  10^'.  Make  JL  vq\n\\  half  a  tread- 
[5^^J  for  the  face  of  No.  18  riso  and  10"  more  to  the  face  of  No. 
19  rise;  draw  the  face  of  No.  10  and  17  rise  directly  ojijiosite  ;  now 
locate  liie  position  of  short  baluster  on  No.  IGand  19  tieads  and 
space  off  the  intermediate  balusters;  tlien  draw  the  face  of  Nos.  17 
and  IS  rise  to  intersect  the  cylinder  and  to  suit  the  balusters;  No. 
17  rise  may  continue  straight  into  tlie  cylinder,  but  No.  18  rise 
should  be  curved  so  that  the  nosing  may  return  without  too  much 
peak  at  the  miter. 


70  Plate  15. 

The  face  of  No.  16  and  19  rise  are  V  from  the  joint  or  spring 
of  cylinder. 

Fig.  6.    Exhihits  a  12"  cyHrifMr. 

The  treads  are  sliowu  10^^;  the  stretchout  CJ  for  the  quarter 
circle  is  found  in  the  same  manner  as  at  Fig.  1.  Only  in  this  case 
observe  the  stretchout  is  for  the  center  line  of  rail  instead  of  the 
string  line. 

I3y  locating  the  risers  around  the  string  line  in  the  cylinder 
gives  the  true  inclination  on  the  string  line,  thus  allowing  the 
veneer  to  be  straight;  having  no  easing  in  case  the  cylinder  be 
veneered;  by  spacing  off  the  regular  treads  on  the  center  line  of 
rail,  the  -veneer  for  the  face  of  cylinder  will  have  an  eas-ing  above 
and  also  below,  connecting  the  circular  part  with  the  straight ; 
this  gives  to  the  wreath  part  tif  rail  more  inclination, and  thereby 
helps  the  appearance  of  the  rail. 

The  cylinder  is  12"  in  diameter,  and  if  2"x2^^  balusters  be 
required  the  center  line  of  rail  will  equal  Vo'}>i"  diameter,  or  a 
radius  of  Q%".  Here  the  face  of  Nos.  i:5  and  IG  rise  are  opposite, 
and  '^li"  from  the  joint  or  spring  of  cylinder. 

Now  locate  the  short  baluster  on  No.  13  and  16,  treads  and 
space  off  the  intermediate  balusters  around  the  cylinder,  then 
curve  No.  14  and  15  rise,  to  suit  the  balusters  at  M  and  N. 

The  intersection  of  No.  14  rise  is  made  opposite  that  at  N; 
the  rise  No.  14  is  termed  a  "concave  rise,"  and  No.  15  rise  is 
termed  is  a  "  convex  rise." 

Pig.  7.  Shows  the  treads  laid  off  on  the  center  line  of  rail 
for  a  cuUnder  14"  in  dhwietcr. 

The  dotted  line  shows  the  center  line  of  baluster,  and  is 
struck  with  a  radius  of  1%"\  the  tread  is  \0",  JCis  the  stretch- 
out for  the  quarter  circle  PNF.  Make  JL  equal  half  a  tread 
[5'^]  for  the  face  of  No.  16  rise,  and  to  No.  17  rise  to  equal  10^''; 
draw  No.  15  and  14  rise  opposite.  Now  take  LC  as  a  radius,  and 
the  verge  of  baluster  at  N  for  a  center,  draw  arc  to  intersect  BC 
prolonged  at  F;  then  FN  will  equal  the  radius  of  curve;  find 
point  on  the  opposite  side  in  same  manner  for  No.  15  rise;  the 
face  of  No.  14  and  17  rise  are  2%"  from  tlie  spring  of  cylinder. 

Fig.  8.  Shous  the  treads  laid  off  i)i  the  cylinder  on  the 
center  line  of  rail  in  the  same  manner  as  at  Fig.  7;  the  face  of 
No.  12  <ind  15  rf.se  arc  shown  1"  from  the  spnng  of  cylinder; 
this  cylinder  is  IQ"  in  diameter. 

Pig.  9.  Exliibits  the  vninner  of  localimj  the  treads  on  the 
center  line  of  rail  for  a  cylinder  of  20"  diameter. 

The  l)alusters  being  2"x2"\  then  the  radius  for  the  center 
line  <»f  rail  will  equal  1Q%";  the  treads  are  11'^  'With  O  as  a 
center  and  OB,  !'<}%"  for  a  radius,  draw  the, center  line  of  rail 
BFC;  the  solid  line  indicates  the  face  of  cylinder.  JJraw  the 
diametin-SOCindeiinite,  iierpendicularto.BC'draw  OF,  alsoJSA 
and  CD  indefinite;  willi  j'as  a  center  and  FO  for  a  radius,  draw 
arc  intersecling  the  center  line  of  rail  at  i?,  through  if  and  jP, 
draw  a  line  to  intersect  CB  and  DC  prolonged  at  K  and  J.  Then 
the  point  if  is  the  focus  and  JC  is  tlie  stretchout  for  the  quarter 
circle  CNF;  set  oif  from  J"  to  i  liaif  a  tread  [5)^^^]  to  the  face 
of  No.  16  rise;  from  that  set  oil  No.  17  and  18  riser  as  shown, 
draw  the  face  of  Nos.  l:J,  14  and  15  rise  opposite. 

Now  locate  the  short  balusters  on  Nos.  I'd  and  18  tread,  and 
space  off  the  intervening  balusters  to  suit;  then  witli  tlie  side  of 
baluster  at  iVas  a  center,  and  LR  for  a  radius,  draw  arc  to  inter- 
sect JBC  prolonged  at  F.     With  JP  as  a  center,  draw  arc  from  L 


Pl^AIE    15.  71 

through  JV  to  intersect  the  cylinder  line  for  the  convex  rise; 
repeat  the  operation  for  the  concave  rise  from  tlie  point  M  on  the 
opposite  side.  The  face  of  No.  13  and  18  rise  are  sliown  10^^  from 
tiie  spring  of  cylinder. 

Pig.  10.  Shrnrs  hov:  to  place  the  risers  in  ci  qiuiHcr  cylin- 
der so  that  the  xvrcath-piece  may  he  constructed  loith  the  least 
expense. 

Draw  the  right  angle  OA  and  OC.  The  radius  OX  for  the 
cylinder  line  equals  6^',  the  balusters  being  '3^^x2^^  then  the 
radius  OA  for  the  center  line  of  rail,  will  equal  M^^  more,  or  G>^''^ 

The  solid  line  shows  the  string  line,  and  the  dotted  line  indi- 
cates the  center  of  baluster,  which  is  the  center  of  rail. 

Draw  the  tangents  AJB  and  CB,  forming  the  right  angle  at 
S;  from  B  set  off  half  a  tread  [5^^]  each  way  on  the  tangents  for 
the  face  of  No.  12  and  13  rise;  set  off  No.  11  and  14  rise,  to 
equal  a  tread  \10^^\  as  shown;  observe  the  face  of  No.  11  and  14 
rise,  both  cut  the  front  string  8}4^^  from  the  spring  of  cylinder  on 
either  side. 

Now  locate  the  short  baluster  on  No.  11  and  14  treads,  and 
space  off  the  intervening  balusters  around  the  cylinder,  then  curve 
No.  13  rise  to  suit  the  baluster;  No.  13  rise  in  this  case  may  run 
in  straight  or  may  be  curved  also,  as  the  stair-builder  may  desire. 

Pig.  11.  Shows  a  quarter  cylinder  of  8'^  radius,  the  solid 
line  being  the  face  of  string,  and  the  dotted  line  indicates  the 
cente)'  line  of  rail. 

The  radius  OA  equals  %%'^\  AB  and  JSCshow  the  tangents 
forming  a  right  angle  at  B.  For  want  of  room,  tlie  face  of  No. 
14  rise  is  placed  at  the  point  B;  then  from  B  set  off  on  the  tan- 
gents a  full  tread  either  way,  as  No.  13  and  15  rise;  draw  them  in 
to  Intersect  the  outer  strings,  and  at  right  angles  to  the  same. 
Now  space  off  the  balusters  in  the  cylinder  and  curve  No.  14  rise 
to  suit  the  baluster;  take  a  tread  [10'^],  for  a  radius,  and  say  at 
J?  as  a  center,  draw  arc  at  P;  then  B  for  a  center,  draw  the 
curve  for  No.  14  rise;  the  face  of  Nos.  13  and  15  rise  is  Hi''  from 
the  joint  of  quarter  cylinder. 

Fig.  12.     Shows  a  quarter  cylinder,  the  radius  being  10". 

If  'y'x2,"  balusters  be  used,  then  the  radius  for  the  center 
line  of  rail  will  equal  iOyi",  .hs  shown  by  the  dotted  Ihio.  Draw 
the  tangents  AB  and  BC,  forming  a  right  angle  at  B;  the  spac- 
ing of  the  treads  in  the  upper  lliglit  of  stairs  locates  No.  10  rise 
on  the  tangent  BC,  two  [■//']  inches  from  the  angle  at  B;  the 
regular  tread  being  10^^,  then  the  face  of  No.  15  rise,  from  the 
angle  at  B  on  the  tangent  AB,  must  equal  8^^,  or  the  difference 
between  BD  and  the  regular  tread  which  eciuals  [10—2=8] 
eight  inches. 

Set  off  No.  14  and  17  rise  to  equal  10'^  each;  the  face  of  No. 
14  rise  cuts  the  string  V  from  tlie  spring  line.  Mark  the  posi- 
tion of  No.  1  and  0  baluster;  then  space  the  intervening  Ijalui!,- 
ters  Nos.  2,  3,  4  and  5  eciually,  and  draw  the  face  of  No.  15  and 
16  rise  into  the  cylinder  to  suit  the  balusters.  Tiiefaceof  No.  15 
rise  C(mtinucs  straiglit  into  the  cylinder,  and  tlie  face  of  No.  10 
rise  requires  to  be  curved.  AVith  the  regular  tread  [10'^]  for  a 
radius  and  a  point  at  the  verge  of  No.  4  baluster  at  F,  draw  arc 
cutting  No.  17  rise  at  H,  from  H  draw  the  curve  tangent  to  No. 
16  rise  to  inters(!ct  the  face  of  cylinder.  The  curving  of  the 
risers  is  discretionaiy  with  the  workman;  the  curve  may  be  more 
or  less;  they  should  be  tlrawn,  however,  so  that  they  wiil  miter 
with  the  return  nosings  without  too  much  peak  at  the  point  of 


72  Plate  15. 

miter.  The  above  quarttr  cylinders  we  have  first  deciderl  on  the 
radius  of  curve,  this  need  not  be  tlie  rule;  for  the  position  of 
risers  may  be  first  dot^ided  upon,  then  afterward  the  radius  of 
quarter  circle  as  described  at  Fig.  13. 

Fig.  13.  Shoivs  how  to  place  the  risers  in  a  quarter  turn, 
so  that  one  lorcatU  will  he  rc<iuircd,  and  from  the  least  possible 
thickness  of  stuff. 

Draw  BA  and  BC  at  rii,'lit  angles  and  of  indefiuite  length; 
from  B  set  off  half  a  tread  i}.'^  on  th(!  line  BA  and  SC  lor  the 
place  of  No.  12  and  i:]  ris<>;  then  niakc^  Xo.  11  and  14  rise  eiiual 
a  regular  tread  'J'^  as  sliown.  Draw  the  face  of  No.  11  and  11 
rise  at  right  angles  to  BA  and  BC, 

Now  decide  upon  the  radius  of  quarter  cylinder,  say  10'^,  and 
the  balusters  being  2^^x2^^  which  will  make  the  radius  for  t!ie 
center  line  of  rail  equal  l()'/</\  Then  make  SZ)  and  jB^eacIi 
equal  10%^^;  draw  i30  and  JF'O  at  right  angles  to  ^C  and  JE>A; 
with  O  as  a  center,  draw  the  curve  i\o\n  D  to  J' for  the  center 
line  of  rail.  The  solid  line  shows  the  face  of  cylinder  the  radius 
of  which  is  %''  less  or  10^^.  The  face  of  No.  11  and  11  rise  ai'e 
'iX^^  from  the  spring  of  cylinder.  Mark  the  center  of  No.  1  and 
0  baluster,  then  space  off  the  intervening  balusters  2,  3,  4  and  5, 
equally  on  the  center  line  of  rail  and  curve  No.  12  and  1.3  rise  to 
suit  the  balusters  as  explained  at  Fig.  12, 

Fig.  14.  Exhibits  how  to  place  the  risers  in,  a  quarter  circle, 
so  that  two  vjrcath-plcccs  may  be  required,  ami  that  they  mny  be 
worked  from  the  plaidi  wUh  the  Icnxt  pi>H>^lblethl<:kncxs<if  Hluff. 

Draw  the  right  angle  OA  and  OB  indefinite  ;  make  OA  e(pial 
the  radius  fl2'^%J  for  the  center  line  of  rail,  draw  tiie  cen.ter  line 
of  rail  ACB;  the  solid  line  shows  the  face  of  cyliiuler,  the  radius 
of  which  is  %''  less  or  12^^  liisect  the  center  line  of  rail  ACB 
at  C,  draw  OC;  at  right  angles  to  OCdraw  the  tangent  CD  arrd 
CF;  also  draw  tangenls  A  J' and  BD  at  right  angles  to  tlie  radial 
lines  BO  and  AO.  Prolong  DB  and  FA  for  the  direction  of 
tjtraight  siring. 

The  v/idth  of  tread  is  IF^;  tlicn  set  off  from  C  on  the  tan- 
gents half  a  tread  [53^^^  1  each  way  for  liie  face  of  No.  14  and  U> 
risers;  again  set  olf  a  regular  tread  |  ll''^]  each  way  for  the  face  of 
No.  13  and  16  risers;  drav/  the  face  of  No.  13  and  14  rise  at  rigiit 
angles  to  the  face  of  string  as  shown;  ol)serve  the  risers  cut  the 
face  string  iV  from  the  spring  of  quarter  circle  on  each  side.  Now 
locate  No.  1  and  7  baluster,  and  space  the  intermediate  balusters 
2,  3,  4,  .5  and  6,  eciually;  then  curve  No.  14  and  15  risers  to  suit 
the  balusters  as  shown. 

Hoirio  stuir-buildors  prof(!r  to  yihira  the  risers  in  this  way  in  a 
(|iiiiitor  circle,  unci  iiiiikin-;-  llio  v/ix'!i.th  in  two  pieces,  lo  relievts  tliu 
eiising  on  the  lower  ed^e  of  the.  ((Uintci' cylinder,  paiticularly  wlien 
llin  balusters  arc  over  2"  in  dituneler;  by  plii.<'in^  llie  risers  as  shown 
ut  FiR.  14,  loss  abruptness  is  cucountered  iil  the  johiing  of  tlie  cylin- 
der with  the  straight  string. 

Fig.  15.  Shows  hoxo  to  lay  off  a  veneer  lohen  there  arc 
xvindcrs  Ui  tlie  culindcr. 

The  plan  of  cylinder  is  13'^  in  diameter.  IIow  to  place  the 
winders  so  as  to  form  an  agreeable  easing  above  and  below  at  the 
connection  of  the  straight  willi  the  circular  part  of  outer  string.* 

*This  inetliod  of  graduating  the  .steps  around  tlic  cylinder  does 
not  govern  the  pitch  of  rail.  Tlic  stair-builder  lias  to  raise  the  incli- 
nation of  tangents  to  make  the  height  of  rail  agreeable  for  tho.se  pas- 
sing up  or  down;  tliis  graduating  of  the  steps  is  to  form  a  pleasing 
easing,  connecting  the  straight  string  v/ith  the  cylinder. 


-»  i'l.ATK    10.  VS 

AB  equals  the  diameter  13'^,  AC  and  BD  indicates  the 
straight  string;  with  A  and  B  for  centers,  and  AB  as  a  radius, 
draw  arcs  intersecting  at  F;  parallel  with  AB  draw  Jf J"  indefi- 
nite, so  as  to  tangent  the  curve  at  L.  From  F  and  through 
points  B  and  A  draw  lines  to  intersect  the  tangent  line  at  H  and 
J;  then  JH  is  the  stretchout  for  the  semi  circle  ALB. 

Fig.  16.  Shows  the  elevation  of  riscru  and  iiuinner  if 
raduatlnfi  the  ividth  of  winders  at  the  narrow  end. 

At  right  angles  to  HJ  draw  JG  equal  to  the  height  of  six 
risers,  more  or  less,  as  the  case  may  be.  Join  GH.  At  H  place 
the  pitchboard  and  draw  the  inclination  HK,  also  place  the  pitch- 
board  at  G  and  draw  tlie  true  inclination  GM  for  the  straight 
string;  bisect  the  angles  at  if  and  Gr.  draw  tlie  curves  2,  Sand 
QXR  at  will,  the  worivman  using  his  judgment  as  to  the  amount 
of  curve  that  will  suit  best.  Now  draw  Nos.  13,  13,  14.  15,  1(5,  IT, 
and  18  treads  to  intersect  the  mixed  lineiTa,  3,  Q,  X,  R.  and 
M.  From  the  intersections  draw  the  riser  liues  parallel  to  JG  to 
intersect  the  stretchout  HJ&t  5,  6,  7,  8  and  9,  from  which  draw 
lines  to  the  focus  F,  intersecting  the  cylinder  line  at  a,  b,  c,  d 
and  e  for  the  location  of  the  face  of  risers  graduating  them  on 
plan.  Fig.  15,  agreeable  to  the  curve  in  elevation  Fig.  16  as 
shown.  The  face  of  No.  12  and  18  rise  is  3^'  from  the  spring  of 
cylinder;  No.  11  and  18  treads  are  each  9^^  wide,  No.  10  and  19 
treads  are  the  regular  width  11^^  Now  locate  the  center  of  short 
baluster,  on  No.  11  and  19  treads  and  space  of  the  intervening  bal- 
usters on  the  center  line  of  rail,  shown  by  the  dotted  line  C7D, 
the  face  of  risers  may  be  shifted  a  little  to  suit  the  balusters  as 
shown  at  a  and  d,  also  No.  18  rise  is  shifted  H^'  to  suit  the  baluster. 
From  the  internal  angle  of  rise  and  tread.  Fig.  10;  set  otf  the  width 
of  string  and  draw  the  lower  edge  of  string  to  please  the  eye  as 
shown  by  the  dotted  line  YXO;  the  veneer  should  be  laid  otf 
with  lead  pencil  so  as  not  to  abraid  the  surface  of  veneer  that 
would,  when  bending  the  veneer  over  a  drum,  cause  fracture; 
neither  should  the  veneer  be  notched  out  for  the  treads  and  risers 
until  the  cylinder  is  taken  from  the  drum;  XX  shows  the  length 
of  staves  in  the  rough. 

These  cyliuders  may  be  constructed  in  different  ways;  there  is 
more  economy  in  the  use  of  staves;  !?*Jod  glue  and  very  dry  mate- 
rial should  be  used:  for  painted  work  use  soft  pine  for  staves.  For 
hard  wood  finish,  the  veneered  cylinder  makes  the  best  and  most 
finished  work,  but  the  expense  is  greater.  For  the  thickness  of 
veneer  see  letter  press  for  Plate  28. 


PLATE  16. 

Plate  16.  [Scale,  %  ^^=i  foot] .  Exhibits  the  construction 
of  a  face-mould  for  a  wreath-piece  landing  on  the  level;  also 
staHini)  from  the  level  to  rake,  the  tangents  on  plan  being  either 
at  right  angles,  acute  or  obtuse.  Also  shows  how  to  place  the 
risers  in  the  cylinder  at  Vie  starting  or  landing,  so  as  to  make 
one  face-mould  answer  for  both  ivrcath-pieces. 

Figs.  1,2,3  and  4.  Slwws  the  plan,  elevation  a^id  face- 
moulds  for  a  wreath  landing  on  the  level. 

The  tread  is  9^^  by  S'^  rise.  The  face  of  No.  16  rise  is  B^^ 
from  the  spring  of  cylinder,  and  hence  the  face  of  No.  17  rise 
must  be  in  the  cylinder  6'^;  the  balusters  are  2^^  diameter,  and 

& 


74  Plate  16. 

the  rail  double  moulded,  3''  wide  aud  \"  deep;  the  cylinder  is 
\Qyi"  in  diameter,  then  the  radius  for  the  center  line  of  rail  will 

equal  ^^^=^M"^%^^"\  six  inches  [6^^].  Then  with  ^" 
as  a  radius,  and  O  for  a  center,  draw  the  semi-circle  A  CJE7;  en- 
close the  semi-circle  with  the  rectilineal  parallelogram  ABDE; 
draw  OC  perpendicular  to  AE,  and  we  liave  the  tangents  AB, 
BC,  CD  and  DE  on  plan;  draw  the  chord  AC;  prolong  tangent 
BA  and  DE  to  the  left  for  the  direction  of  straight  rail. 

Pig.  2.    Exhibitsthedevelopmcntandelcvationof  tangents. 

Let  XX  indicate  the  edge  of  drawing  board;  make  AB,  BC, 
CD  and  DE  equal  tangents  AB,  BC.  CD  and  DE  on  plan,  Fig. 
1;  from  the  points  A,  B,  C,  D  and  E  draw  perpendiculars  to 
XX  indefinite. 

Now  elevate  Nos.  15,  16  and  17  treads  and  risers,  keeping  tlie 
face  of  No.  16  rise  3'^  from  the  spring  line  at  A;  tlirough  the 
center  of  baluster  OO  draw  the  under  side  of  rail;  parallel  witli 
OO  draAV  the  center  of  rail,*  cutting  the  perpendiculars  at  iJand 
J,  From  the  floor  line  set  up  4^'  to  under  side  of  rail,  and  half  the 
depth  of  rail  more  [3^'J  to  the  center  of  level  rail;  parallel  to  XX 
draw  the  center  of  level  rail,  cutting  the  perpendiculars  at  if  aud 
L.  Draw  LJ  prolonged  to  M,  and  cutting  the  per))endicular 
from  Cat  N;  through  N,  and  parallel  to  XX.  draw  WIR,  cutting 
the  perpendiculars  at  JPand  Q;  prolong  HJ  to  intersect  WR  at 
G;  parallel  to  XX  draw  HS,  cutting,'  BP  at  T;  then  NS  is  the 
height  for  the  lower  wreath-piece,  and  RKis  the  height  for  the 
upper  wreath-piece;  prolong  HS  to  E,  then  EL  will  be  the 
whole  height.  Make  J?!/ equal  the  chord  AC,  Fig.  1;  from  IF, 
aud  at  right  angles  to  tangent  iVJ"  prolonged,  draw  TV;  from  P, 
and  at  right  angles  to  tangent  HJ  prolonged,  draw  B'i;  parallel 
to  BP  draw  the  half  width  of  rail  [IM^'J,  cutting  the  tangents  at 
3  and  4  for  the  increased  width  of  mould  on  the  radial  Hues; 
make  J? j^  equal  the  chord  AC,  Fig.  1. 

Bevels.  Make  ab  parallel  to  XX;  at  right  angles  to  XX 
draw  dh  equal  to  the  radius  OC,  Fig.  1;  make  d  7  equal  TV: 
aud  d  G  equal  P2,  also  make  d  5  equal  the  height  RK;  draw  h 
7,  ii  6  and  h  5  prolonged  to  XX. 

'     Fig.  3.    Exhibits  the  face-mould. 

Let  AB  equal  HJ,  Fig.  2;  with  A  as  a  center,  and  Wt^,  Fig. 
2.  for  a  radius,  draw  arc  at  C:  again,  with  J3  as  a  center,  and 
NJ.  Fig.  2,  for  a  radius,  draw  arc  intersecting  at  C.  Join  BC. 
Parallel  to  AB  and  CB,  draw  the  radial  lines  CO  and  AO  for  the 
parallelogram  ABCO  on  the  cutting  plane  that  will  coincide  with 
the  parallelogram  ABCO  on  plan  when  in  position. 

Proof.  The  diagonal  BO  must  equal  MU,  Fig.  2,  if  so,  thf 
angle  of  tangents  at  JB  is  correct.  Prolong  tangent  BA  6'^  to  F: 
make  joints  at  F  and  C  at  right  angles  to  tangents  BA  and  BC. 
Make  AD  equal  JG,  Fig.  2;  draw  DO  for  the  direction  of  minor 
axis;  make  CS  and  C  3  each  equal  J  4,  Fig.  2,  also  make  A  4, 

*Let  it.  he  okserved  right  here  that  for  all  wreaths  .startiug  from 
Ihe  level  to  rake,  or  those  from  the  rake  to  a  level,  and  also  turn- 
outs at  the  newel,  and  wreaths  on  winders;  also  platform  wreatb.s, 
when  it  is  refiuired  to  find  the  length  of  odd  balusters.  In  all  such 
cases  the  center  line  of  rail  must  be  drawn  In  this  way  to  obtain  the 
correct  bciglit  for  each  wreath-piece.  For  platform  wreatlis,  when 
the  length  of  odd  balustei-s  is  not  required,  the  center  line  of  rail  may 
be  drawn  at  once  from  the  external  angle  of  .step  and  rise,  for  the 
inclination  of  tangents  and  height  of  wrcath-picce  as  shown  at  Fig. 
2,  Plate  29.    , 


Plate  16  75 

A  5,  each  equal  J 3,  Fig.  2.  Let  O  8  equal  the  radius  OC,  Fig. 
1,  for  the  length  of  senii-iiiinor  axis;  make  8  6  and  8  7  each  equal 
the  half  width  of  rail  [IH^'J. 

Parallel  vfith  AJPdraw  5  10  and  4  9  for  the  shauk  of  mould, 
Now  pivot  the  trammel  in  O  with  the  arms  at  right  angles  to  O  S; 
then  set  from  pencil  to  minor-pin  the  distance  O  7,  place  the 
pencil  in  the  point  at  3,  drop  the  pins  in  the  grooves,  and  fasten 
the  major-pin;  then  trace  the  curve  for  the  convex  side  of  mould 
through  the  points  5,  7,  3:  again,  set  from  pencil  to  minor-pin  the 
distance  O  6,  place  the  pencil  in  the  point  at  2,  and  drop  the  pins 
in  the  grooves,  then  fasten  the  major-pin  and  trace  the  curve 
through  the  points  4,  6,  2,  for  the  concave  side  of  face-mould; 
proceed  in  like  manner  to  trace  the  center  line. 

The  section  at  M  shows  the  bevel  found  in  the  angle  at  7, 
Fig.  3,  applied  from  the  far-e  of  crook  so  as  to  pitch  tlie  joint  at 
F  down;  the  section  at  iVsliows  the  bevel  found  in  the  angle  at 
6,  Fig.  2,  applied  so  as  to  pitch  the  joint  at  C  up;  the  block  pat- 
tern shows  the  section  of  rail  when  squared  up,  the  shaded  parts 
indicate  the  surplus  wootl  that  has  to  be  removed  in  the  formatiou 
of  wreath-piece. 

-■  Fig.  4.  Slunvs  tlic  face-iuoxild  for  the  wvcatli-piccc  on  Ihc 
level. 

Draw  the  right  angle  EDC,  make  DC  equal  NL,  Fig.  ;J. 
make  J) J^  equal  ED  on  plan.  Fig.  1.  Parallel  with  DE  and  DC 
draw  CO  and  EO  for  the  parallelogi'am  OCDE  on  the  cutting 
plane,  or  plane  of  plank. 

Proof.  The  chord  EC  and  also  the  diagonal  OD  in  this  case 
must  cijual  KY,  Fig.  2;  prolong  tangent  DE  to  i^'o".  Make 
joint  at  F  s(iuare  to  DF\  make  C2  and  Co  each  eriual  the  half 
width  of  rail  [1H^'][  let  E  4  and  E  5  each  eijual  J  3,  Fig.  2. 
Parallel  to  EF  draw  4  6  and  5  7,  for  the  shank  of  mould;  as  th<' 
difference  between  the  semi-minor  axis  OC  and  the  semi-major 
axis  OE  is  so  little,  the  comi)asscs  will  suit  best  to  draw  the 
concave  and  convex  curves  as  shown i.  The  .section  at  i!f  shows 
the  bevel  found  in  the  angle  at  5,  Fig.  2,  applied  so  as  to  pitch 
the  joint  at  C  down;  (he  section  at  iV" shows  tlie  square  applied 
allowing  the  shank  FE  to  have  a  horizontal  position.  The  block 
]  atteni  is  applied  at  right  angles  to  the  line  made  from  the  bevel 
showing  the  twist  of  rail  in  the  crook  at  the  joint. 

Figs.  5  and  6.  Sho^r  how  fo  place  the  risers  in  the  cylin- 
der for  a  tDvaith.  siarling  from  the  lei^ei,  so  as  to  iiwlce  thefacc- 
Moidds  draivn  for  Fig.  1  answer  for  Fi'j.  5. 

Fig.  5.     ShoHS  the  plan. 

The  tangents  AJ5,  BC,  CI?  and  i).£7  enclosing  the. semi-circl« 
ACE,  coincide  with  plan,  Fig.  1,  Prolong  tangents  BA  and 
DE  to  the  right,  for  the  direction  of  straight  rail;  the  radius 
OC  for  the  center  line  of  rail  equals  6'''. 

Fig.  6.  Sfiows  Ute  elevation  and  development  of  tangents, 
and  also  the  treads  and  risers. 

Let  XX  indicate  the  edge  of  drawing  board;  make  AB,  BC, 
CD  and  DE  equal  tangents  AB,  BC,  CD  and  DE  ou  i)lau.  Fig. 
.5.  From  A,  jB.  C,  D  and  -E7  erect  perpendiculars  to  XX  indefi- 
nite; let  XX  also  indicate  the  floor  line;  from  the  floor  line  set  up 
4"'  to  the  under  side  of  rail,  and  the  half  depth  of  rail  [2^^]  addi- 
tional, making  6"  fnmi  the  floor  to  the  center  of  rail  as  shown  ou 
the  left.  Parallel  with  XX  draw  the  center  of  rail  cutting  the 
perpendiculars  in  F,  G,  H,  J" and  K;  make  KL  equal  EL,  Fig. 
3,  ft)r  the  wIm.u-  i.<ii;i,(  that  bolh  wreath  pieces  have  to  raise,     i. 


76  Plate  16. 

Now  through  the  point  L  draw  the  iuelinatiou  for  the  ceuter 
of  rail,  cutting  the  perpendicular  from  B  VitM;  join  MG,  cutting 
the  perpendicular  from  C  at  N;  from  N  and  parallel  to  XX  draw 
NS;  parallel  to  the  center  line  of  rail  ML  produced,  draw  the 
under  side  of  rail  PQ.  From  XX  on  the  floor  line  set  up  the 
height  of  No.  1  and  No.  3  rise;  draw  No.  2  tread  at  riglit  angles 
to  AL,  cutting  the  under  side  of  rail  at  O,  then  O  is  the  center  of 
baluster,  and  if  the  baluster  is  2^^x2'^,  then  the  face  of  No.  2  rise 
will  be  V  to  the  left,  making  the  face  of  rise  ^H'^  from  the 
spring  line  AL  of  cylinder,  as  shown. 

Now  return  to  plan.  Fig.  5;  make  the  face  of  No.  2  rise  2)4^'' 
from  the  spring  line  AE;  set  off  to  No.  1  rise  to  equal  a  tread 

Mark  the  ceuter  of  baluster  on  No.  2  tread,  from  that  space 
off  the  balusters  iu  the  cyliuder;  then  draw  thecouvex  rise  to  suit 
as  shown. 

It  will  be  observed  now  that  the  height  LS,  P'ig.  6,  agrees 
with  the  height  NS,  Fig,  2,  and  the  height  NH.  Fig.  G,  agrees 
with  the  height  KR.  Fig.  2,  hence  one  set  of  face-moulds  and 
bevels  will  answer  tor  both  wreaths,  starting  and  lauding. 

Pigs.  7,  8  and  9.  Exhibits  the  plan,  elevation  and  face- 
mould  for  a  vjreath-piece,  starting  frovi  the  level  to  a  rake,  the 
angle  of  tanyeiits  on  plan  being  obtuse.  Fence  the  circle  on  plan 
is  less  than  a  quarter  circle.  Tl\e  regular  tread  is  10"  and  rise 
1",  the  balusters  are  Z"y,2"  and  the  rail  is  4"  wide  by  2^^" 
deep.  How  to  place  the  risers  in  the  cylinder  so  that  the  vjreaih- 
piece  ivill  raise  on  the  level  to  the  proper  height  for  tlw  long  bal- 
usters. 

Fig.  7.     Erhibits  the  plan. 

AB,  BC  shows  the  tangent?.  Prolong  tangents  BA  and 
BC  for  the  direction  of  straight  rail.  From  A  aiid  C  draw  dotted 
lines  at  right  angles  to  the  tangents  BA  and  JBC  intersecting  at 
O;  parallel  with  tangents  BA  and  BCdraw  CD  and  AD  for  the 
parallelogram  ABCD  on  plan.  From  A  and  at  right  angles  to 
CB  produced,  draw  AF;  from  the  ceuter  0  draw  the  ceuter  line 
of  rail  from  A  to  C 

Fig.  8.  Exhibits  the  development  and  elevation  of  tangents 
front  ivhirli  to  find  the  face-mould  and  position  of  No.  2  rise  on 
plan.  Fig.  7. 

Let  XX  indicate  the  edge  of  board,  and  also  the  line  of  floor. 
Make  CB,  BA  equal  tangents  CB  and  BA  on  plan,  Fig  7;  from 
the  points  CBA  erect  pei-pendiculars  to X.X  indefinite;  from  XX 
.set  up  half  a  rise  \y}i"]  to  the  underside  of  rail,  and  1  }i/'  addi- 
tional or  ^lH"  to  the  center  of  rail  at  i?;  from  Z)  and  parallel  XoXX 
draw  Z).E7  through  E,  draw  the  true  inclination  of  the  center  Une 
of  rail  indefinite,  cutting  the  perpendicular  from  C  at  H;  par- 
allel to  EH  prolonged,  draw  the  undeiside  of  rail;  from  JCXset 
up  the  height  of  No.  1  ri.se  "t";  parallel  to  XX  draw  No.  1  tread, 
intersecting  the  miderside  of  rail  at  O.  Then  O  is  the  ceuter  of 
baluster;  as  the  balusters  are  2''^x2'',  then  the  face  of  No.  1  rise 
will  be  one  inch  [V]  to  the  left  of  O,  or2>:j'^^  iu  the  cyliuder,  and 
as  the  treads  are  W  the  face  of  No,  2  rise  will  be  7>^'^  from  the 
spring  line  of  cylinder  as  shown. 

Thus  estabiishing  the  location  of  risers  so  as  to  give  the  proper 
hcvjht  to  the  wreath-piece  as  required;  from  iJand  parallel  to  XX. 
tli-aw  HJ,  cutting  the  perpendicular  from  B  at  K;  thou  EK  is 
the  height  that  the  v.'reath-piece  has  to  raise. 

Make  EL  equal  BF,  Fig.  7,  from  L  and  at  right  angles  to 
!£■.&  prolonged,  draw  LM\  make  JiV equal  the  chord  AC,  Fig.  7 


I'l.ATK   1(>.  TT 

Let  JP  eqnal  the  diagonal  BD,  Fit;-.  7;  prolong  JH  and  make 
JQ  equal  BO  on  plan.  Fig.  7;  tliiough  D  and  P  draw  a  line  to 
intersect  the  perpeudiciilar  from  Q  at  R. 

Bevels.  Draw  the  gange  line  /ST parallel  to  XX\  at  right 
angles  to  XX,  draw  VW  e(iual  to  AF,  Fig.  7.  Wake  T7'4  equal 
LM,  Fig.  S,  let  V  .5  eipial  the  heiijht  EK  in  e'evation,  Fig.  8; 
draw  W  4  and  IT  5  prolonged  to  XX,  parallel  to  ST,  draw  the 
half  width  [:y']  uf  rail,  cutting  the  hypotlienuse  of  bevels  at  6 
and  7. 

Fig.  9.     Exhibits  the  fncc-mouhl. 

Make  AB  equal  ^iJ,  Fig,  8;  with  A  as  a  center  and  DN, 
Fig.  8,  for  a  radius,  draw  arc  at  C:  again,  with  S  for  a  center  and 
tangent  AB,  Fig.  7,  for  a  radius,  draw  arc  inteisecting  at  C, 
Join  BC.  I'aralhd  to  AB  and  BC,  draw  CD  and  AD  for  the 
parallelogram  ABCD  on  the  cutting  plane  or  plane  of  plank. 

P7-oof.  The  diagonal  BD  must  agree  with  DP,  Fig.  8.  If 
so,  the  angle  of  tangents  at  B  is  correct. 

Prolong  tangent  BA,  G"  to  F;  also  prolong  the  level  tangent 
BC,  ^"  to  H\  make  joints  at  J' and  iT  at  right  angles  to  tiie  tan- 
gents as  shown;  fi'om  Cand  at  right  angles  to  tangent  BC,  draw 
CJ  indefinite;  prolong  the  diagonal  BD  to  intersect  CJ"  at  0\ 
th-aw  the  radial  line  AO  for  the  point  of  tangency,  or  the  intersec- 
tion of  straight  shank  with  the  curved  part  of  face-monld;  for  I'ROok 
that  the  intersection  at  O  is  correct,  the  diagonal  OS  must  equal 
DR,  Fig.  8.  Make  F  2  and  Fi  each  equal  4-6,  Fig.  8;  also  make 
C  4  and  C  .5  each  eciual  .5-7,  Fig.  8;  parallel  with  FB,  draw  3-!» 
and  2-8;  parallel  with  CH  draw  .5-7  and  4-G;  at  right  angles  to 
OC  draw  OK  eqnal  to  the  radius  OA,  Fig.  7.  Make  K  1 0  and  K 
11  each  equal  the  half  width  of  rail  [2"];  now  OC  is  the  semi- 
major  axis  and  OiiC  the  semi-minor  axis.  Instead  of  a  trammel 
use  a  straight  edge  to  find  the  elliptic  curves  of  this  face-mould. 
Draw  the  two  right  angles  at  O  to  indicate  the  arms  of  trammel; 
for  the  concave  side  of  mould  take  the  straight  edge  and  mark 
from  the  end  at  8  to  Li,  the  distance  O  10,  for  the  minor  notch; 
again  mark  the  major  notch  at  P  cimal  to  O  4;  now  move  the  rod 
at  intervals,  keeping  the  two  notches  on  the  riglit  angle  lines,  then 
marking  points  at  the  end  of  rod,  through  whichdraw  the  curves, 
using  a  flexible  strip;  proceed  in  like  manner  to  draw  the  center 
and  convex  curves  of  mould.  Points  on  tiie  diagonal  OB  may  be 
found,  giving  three  points  in  the  cune  through  which  to  draw 
the  curves,  and  thus  dispensing  with  the  trammel.  To  find  the 
points  return  to  Fig.  8:  make  Qyequal  to  the  radius  OA.  Fig.  7; 
|.ara!lel  to  JD  draw  YF,  parallel  to  YF  draw  the  half  width  of 
rail  [2^']  intersecting  DR  at  G.  At  Fig  1)  make  B-S  equal  DF, 
Kig.  8;  let  S  12  and  -S  13  each  equal  FG,  Fig.  8,  giving  the  three 
lioints  required.* 

Observe  bevels  as  applied  at  sections  M  and  iV makes  the 
wreath-piece  answer  for  a  landing  on  the  level,  instead  for  a  start- 
ing off  the  level  as  shown  on  plan,  Fig.  7;  by  turning  the  wreath- 
piece  upside  down,  when  squared  up  before  moulding,  it  will  then 
answer  for  plan.  Fig.  7.  The  bevel  applied  at  section  Jlf  is  found 
in  the  angle  at  5,  Fig.  8;  and  the  bevel  at  section  iVis  found  in 
the  angle  at  4,  Fig.  8.  Observe  they  do  not  cross  the  tangents  in 
their  application. 

*The  correct  width  for  any  face-mould  on  the  diagonal  line  was 
first  given  by  Mr.  J.  H.  Monckton.  then  by  Mr.  Secor.  The  above 
method  will  suit  for  small-face  moulds,  but  for  long  moulds  more 
points  iu  the  curve  are  required  as  a  guide  for  the  flexible  strip. 


'-'8  Plate  16. 

Figs.  10  and  11.  Shmvs  hoiv  to  place  the  risers  in  the 
cylinder  so  <is  to  mnke  the  face^nould  for  thej)lan,  Fig.  7,  answer 
for  a  landing. 

Fig.  10.    Shows  the  plan. 

The  radius  for  the  center  line  of  rail,  the  tangents,  and  angle 
of  tangents,  coincides  with  those  of  Fig.  7;  CB  and  BA  are  the 
tangents;  OA  is  the  radius  for  the  center  line  of  rail,  the  dotted 
line  indicates  the  string  line. 

Fig.  11.  Exhibits  the  elevation  and  development  of  tan- 
gents, and  olso  the  landing,  tread  and  rise. 

Let  XX  indicate  the  edge  of  drawing  board;  make  CB  and 
BA  equal  tangents  CB  and  BA,  Fig.  10;  from  the  points  C,  B, 
A,  draw  perpendienhirs  to  XX  indefinite;  anywiiere  on  the  per- 
pendicular from  B  place  the  rise  of  pitchboard,  and  draw  the  true 
inclination  for  the  center  of  rail  as  DFH.  ParalU-l  to  DFH 
draw  the  under  side  of  rail;  parallel  to  XA  draw  iDJ"  prolonged, 
for  the  center  of  level  rail;  now  make  JK  to  equal  4>4^^  for  the 
lloor  line  to  agree  with  AD,  Fig.  H.  Through  K,  and  parallel  to 
XX,  draw  the  floor  line  intersecting  tlie  under  side  of  rail  at  O; 
then  O  is  the  center  of  baluster;  the  baluster  being  2^^  in  diameter 
set  off  1  inch  more  to  the  face  of  rise  marked  No.  15;  draw  No.  15 
rise  at  right  angles  to  XX,  and  set  off  No.  14  tread  and  rise,  thus 
locating  the  face  of  No.  14  rise  S%^^  from  the  spring  line  of  cyl- 
inder. As  the  treads  are  10'''  then  the  face  of  No.  15  rise  will  be 
in  the  cylinder  1^'^  from  the  soring  line.     [W—^%"=\  %'^}. 

Observe  the  height  LF  equals  the  height  KE,  for  Fig.  8. 
Now  return  to  plan.  Fig.  10,  and  make  the  face  of  No.  14  rise 
8%''^  from  the  spring  line  OC;  thus  arranging  the  risers  in  the 
cylinder  on  plan  so  that  the  face-mould.  Fig.  9,  will  also  suit  for 
Ihe  landing  wreath-piece. 

Figs.  12,13  and  14.  Shoirs  the  plan,  eUvation  and  face^ 
mould  for  a  ■wrcatli-inccc,  starting  from  the  level  to  the  ndw,  the 
angle  of  tangents  on  plan  licing  acute;  the  curve  on  plan  being 
greater  than  a  quarter  circle. 

TiuM-egular  tread  is  10^',  the  rise  7^',  balusters  2'^  in  diam- 
eter, and  the  rail  4'^  wide  by  2)4^^  deep. 

How  to  place  the  risers  in  the  cylinder  so  that  the  wreath- 
piece  will  raise  the  proper  height  on  the  level,  for  the  long  balus- 
ters, and  at  the  same  time  be  worked  from  the  least  possible 
thickness  of  plank. 

Fig.  12.    Shows  the  plan. 

AB,  BC  are  the  tangents;  at  right  angles  to  the  tangents, 
draw  AO  and  CO;  from  the  center  O  describe  the  center  line  of 
rail  from  A  to  C;  prolong  the  tangents  for  the  direction  of 
straiiilit  rail.  Draw  the  chord  AC,  from  Cand  at  right  angles  to 
.AJS  draw  CD. 

Fig.  13.  Erhlbits  the  development  and  elevation  of  tan- 
gents, and  also  the  treads  and  risers. 

Let  XX  indicate  the  edge  of  drawing  board  and  also  the  line 
of  floor.  iSlake  AB,  BC  e:\\ml  tangents  AB,  BC on  plan.  Fig. 
12;  draw  perpendiculars  to  JfX  from  the  points  A,  B,  Cindelinite; 
from  XX  set  up  half  a  rise  to  the  underside  of  level  rail  and  1  h^' 
additional  to  the  center  of  rail  at  D;  parallel  with  XX  draw 
DF;  through  F  draw  the  true  inclination  of  the  center  line  of 
rail,  cutting  the  perpendicular  from  A  at  H;  parallel  with  FH 
produced,  draw  the  underside  of  rail.  Now  on  AiT  set  np  the 
height  of  No.  1  and  'Z  risers;  parallel  with  XX  draw  No.  1  and  2 


ri.ATK    16.  Tit 

treads,  cutting  tlie  under  side  of  rail  at  O,  O  for  tlie  center  of  bal- 
uster, as  the  balusters  are  2^\  then  the  face  of  No.  1  and  2  rise 
will  be  V^  to  the  right,  or  the  face  of  No.  3  rise  will  be  4K^^ 
from  the  spring  line  AH;  and  as  the  treads  are  10'^  the  face  of 
No.  1  rise  will  be  53'o^^  in  the  cylinder. 

Now  return  to  plan.  Fig.  12;  make  the  face  of  No.  2  rise4K'''' 
from  the  spring  line;  set  off  the  face  of  No.  1  and  3  rise  and  draw 
them  at  right  angles  to  JBA  prolonged;  locate  the  balusters  at  No  3 
tread  and  space  them  off  around  the  cylinder,  and  curve  No.  1 
rise  to  suit  the  baluster.  Returning  to  Fig.  13  draw  iJJ"  paral- 
lel to  XX,  cutting  the  perpendicular  from  S  at  if,  then  JTfis 
the  height  the  wreath-piece  is  required  to  raise;  bisect  DJ"  at  P. 
Make  JL  equal  HB  on  plan.  Fig.  13;  let  J!2\f  equal  the  chord  AC. 
Fig.  13;  draw  PL  prolonged  to  intersect  the  perpendicular  from 
R&tN. 

Make  FQ  equal  DB,  Fig.  13;  from  Q  and  at  right  angles  to 
i?P  produced,  draw  QS.^ 

Bevels.  Parallel  with  XX  draw  TV;  draw  TW  perpen- 
dicular to  XX,  and  equal  to  DC,  Fig.  12;  make  Ti  equal  SO, 
Fig,  13,  make  T  5  equal  the  height  FK,  Fig.  13.  Draw  W4 
and  TVs  produced  to  XX  for  the  inclination  of  bevels.  Parallel 
with  rVdraw  the  Iralf  width  of  rail,  cutting  the  hypothenuse  of 
bevels  at  6  and  7. 

Fig.  14.    Exhibits  the  eonstructicni  of  face-mould. 

Make  AB  equal  HF,  Fig.  13,  with  A  as  a  center,  and  DM, 
Fig.  13,  for  a  radius,  draw  arc  at  C;  again,  witli  .5  as  a  center, 
and  the  tangent  CB  on  plan.  Fig.  13,  for  a  radius,  draw  arc  inter- 
secting at  C,  draw  BC,  draw  the  chord  AC,  bisect  AC  at  H, 
draw  the  diagonal  .Bi?  prolonged. 

From  C  draw  a  perpendicular  to  tangent  BC,  and  inter- 
secting BH  produced  at  0;  draw  the  radial  line  OA  for  tlio 
trapezium  OABC on  the  cutting  plane,  that  will  agree,  when  in 
position,  with  the  parallelogram  OAJBCon  plan,  Fig.  13. 

Proof.  The  diagonal  BHO  must  equal  PLN,  Fig.  13. 
Prolong  tangent  BA  ^"  to  J"  for  shank;  also  prolong  BC  to 
Z»,  1",  for  straight  wood  to  help  the  easing  at  the  connection  of 
straight  rail.  Make  joints  at  J  and  i  at  right  angles  to  the  tan- 
gents. Let  C3  and  C3  each  equal  5  7,  Fig.  13;  make  J"  4  and 
Jo,  each  equal  4  6,  Fig.  13.  Draw  the  semi-minor  axis  OF  in- 
definite, and  at  right  angles  to  OC,  make  OF  equal  the  radius 
OA,  Fig.  13.  f 

Let  F  10  and  P  11  each  equal  the  half  width  of  rail  [3^'] 
parallel  with  JB  draw  4-6  and  .5-7;  also  parallel  to  LB diaw  3-l» 
and  3-8;  now  place  the  trammel  in  the  point  at  O  with  the  arms 
on  the  semi-major  axis  OC.  Set  from  the  pencil  to  minor  pin  on 
tiie  rod  the  distance  O  11,  then  place  the  pencil  iu  the  point  3, 
drop  the  pins  iu  the  grooves  and  fasten  the  major  pin;  now  trace 
the  convex  curve  through  the  points  7,  11,  3.  Eepeat  the  opera- 
tion for  the  center  and  concave  curves  of  face-mould. 

The  section  at  M  shows  the  bevel  found  in  the  angle  at  4. 
Fig,  13,  and  the  bevel  applied  at  section  JVis  shown  in  the  angle 
at  5,  Fig.  13. 

*The  point  Q  should  be  opposite  the  point  D,  Fig;.  12,  or  to  the  left 
of  the  perpendicular  BK,  as  shown  at  Fig.  2,  Plate  1.3;  the  results  how- 
ever are  the  same  either  way,  for  a  mould  of  this  kind  ha\ing  a  full 
easement.  -     . 


so  Plate  17. 

Pigs.  15  and  16.  Sh9ws  ike  plan  and  elevation  of  a  cylin- 
der landinfi  to  accompany  Figs.  12,  and  13,  which  is  for  a  starting, 
Jlovf  to  jjlace  the  risers  so  that  one  face-mould  will  answer  for  both 
to,  eath-pieces. 

Fig.  15.     Shows  the  plan. 

OC  is  the  radius,  CB  and  BA  are  the  tangents. 

Fig.  16.  Shows  the  develojnne)it  and  elevation  of  tangents 
and  the  trends  and  risers. 

Let  XX  indicate  a  base  line;  malce  AB  and  BC  equal  tan- 
gents AB.  BC.  Fig.  15.  From  the  points  A,  B,  C  erect  perpen- 
diculars to  XX  indefinite;  parallel  to  XX  draw  DF,  from  F 
draw  the  true  inclination  of  the  center  line  of  rail,  cutting  the 
perpendicular  from  A  at  H;  parallel  to  i^iif  produced,  draw  t\w 
underside  of  rail  shown  Ity  the  dotted  line.  INIake  DK equal  FB, 
Fig.  13;  [4M^^]  from  IT  and  parallel  to  XX.  draw  the  floor  line, 
cutting  the  underside  of  rail  at  0,  then  0  is  in  the  center  of 
baluster,  the  baluster  is  2'',  then  the  face  of  landing  rise.  No.  15, 
will  be  V^  to  the  right  of  0.  Now  set  off  No.  14  tread  and  rise 
■which  locates  the  face  of  No.  14  rise  h%''  from  the  spring  line 
AH  of  the  cylinder. 

Parallel  to  XX  draw  HJ;  it  will  be  observed  that  the  height 
JF  is  equal  to  the  heiyht  KF,  Fig.  13,  and.that  they  both  are  the 
same  height  [4%'^]  from  the  floor  line  to  the  center  of  rail. 

Now  return  to  plan.  Fig.  15,  draw  the  face  of  No.  14  rise 
h%"  from  the  spring  line  OA,  then  as  the  regular  tread  is  W\ 
the  face  of  No.  15  rise  will  be  in  the  cylinder  4^'^;  now  space  oft" 
the  balusters  from  No.  14  rise  around  the  cylinder,  then  cun'e  No. 
15  rise  to  suit  the  baluster  as  shown. 


PLATE  17. 


Plate  17.  [Scale  K'"'=l  foot.]  Exhibits  the  construction 
of  a  face-mould,  for  a  quaHer  cylinder  having  flyers  above  and 
below  the  quaiter  pace.  Also  the  face-mould  for  a  wreafh-plece 
staHing  from  a  newel,  the  cylinder  being  less  than  a  quarter 
circle  on  plan. 

Figs.  1,  2  and  3.  Shows  the  plan,  elevation  and  face- 
mould. 

For  a  quarter  circle,  tread  is  W^  and  rise  1^',  the  balusters 
are  S^^xS''^  and  rail  4^'x2X^^. 

Fig.  1.  Slwws  plan  similar  to  Fig.  10,  Plate  15;  the  risers 
are  placed,  in  the  quaHer  cylinder  so  the  ivreath-piece  nmy  he 
worhed  out  in  one  piece,  and  may  luwe  the  same  inclination  on 
tlie  line  of  tangents  as  the  straight  part  of  rail. 

The  radius  OA  for  the  center  line  of  rail  equals  65^^'',  draw 
the  radii  OA  and  OC  at  right  angles;  parallel  to  OA  and  OC 
draw  the  tangents  CB  and  AB,  forming  the  square  parallelogram 
OABC  on  plan;  prolong  tangents  BA  and  BC  for  the  direction 
of  straight  rail,  the  face  of  No.  12  and  13  rise  is  5'^  from  the  angle 
at  B;  No.  11  and  14  rise  is  spaced  off  a  regular  tread  lO^'',  locating 
the  face  of  No,  11  and  14  rise  8K^^  from  the  spring  of  cylinder  at 
A  and  C*  f  ■ 

Often  the  stair  builder  has  to  furnish  rails  to  order  from  the 
country.  In  all  such  cases  he  must  know  the  diameter  of  cylinder, 
height  of  rise,  width  of  tread,  the  location  of  risers  at  the  cylinder, 
if  at  the  spring,  or  out  from  the  same,  size  of  balustera,  also  rail;  if 
the  rail  is  on  the  right  or  left  ascending  the  stairs. 


Plate  17.  81 

Fig.  2.  Sliowfi  the  elevation  and  development  of  tangents , 
also  the  treads  and  risers  from  plan. 

Let  XX  imlicate  the  edge  of  drawing  board.  Make 
AB  and  JBC  equal  tangents  AB  and  .BC  on  plan.  Fig.  1;  from 
the  points  A,  JSand  Cdraw  lines  perpendicular  to  XX  indefinite; 
now  elevate  the  treads  and  risers,  keeping  the  face  of  No.  11  and 
14  rise  81^''^  from  the  spring  lines  A  and  C;  draw  the  true  incli- 
nation of  rail  from  the  external  angle  of  No.  11  and  13  tread  an<l 
rise,  cutting  the  ))erpendiculars  at  D,  J7aud  F.  Parallel  with  XX 
draw  Da,  cutting  the  perpendicular  from  B  at  J";  thenjH!Fis 
the  height  the  wreatli-piece  has  to  raise;  from  J' and  at  right  angles 
(()  2?^ draw  JK;  m;il<c  HL  e(iual  tlie  chord  AC  on  plan.  Fig.  1. 
I'arallel  with  BE  draw  tlie  half  width  of  rail  [2"],  cutting  tho 
inclination  of  rail  at  N. 

Bevels.  As  hoih  tangents  have  the  same  inclination  only 
one  bevel  will  bi'  nvpiircd.  I'arallel  to  XX  draw  PQ;  at  riglit 
a II tries  to  XX  draw  QR  equal  to  the  radius  OC,  Fig.  1;  make 
QS  eqiud  JK,  .Iraw  RS  prolonged  to  XX. 

Fig.  3.     .S/k'I'-s'  tlir  face-mould. 

Let  AB  equal  ED  in  elevation,  Fig.  2;  with  A  as  a  center 
and  tlie  distance  LF.  Fiir.  2,  for  a  radius,  draw  arc  at  C;  again, 
Avith  B  asa  center  and  AB  fnr  ;i  radius  draw  arc  intersecting  at  C; 
draw  BC;  parallel  to  taiii^ent  BA  and  BC,  draw  the  radial  lines 
CO  and  AO  for  the  parallelognim  OAJSC on  the  cutting  plane. 

Proof.  The  diagonal  BO  must  equal  the  diagonal  BQ 
on  J  dan.  Fig  1. 

Prolong  tangents  BA  and  BC  H'^  to  D  and  JE7for  the  length 
of  shank;  make  joints  at  JDand  E  at  right  angles  to  .BI?  and  BE. 
Draw  the  diagonal  BO  for  the  direction  of  minor  axis;  draw  FH 
indefinite  through  O  and  at  right  angles  to  OB  for  the  direction  of 
major  axis. 

Make  OJ'equal  the  radius  OC,  Fig.  1,  for  the  length  of  semi- 
minor  axis;  h'\.  J r,  and  J"?  eacli  e(jual  the  half  widthof  rail  ['J'''); 
make  A  'J  ami  A  S  also  C4  and  C5  each  e(pia]  i7JV,  Fig.  2.  Par- 
allel with  J5.E7and  BD  draw  .5-t)  anrl  4-8,  abso  8 -11  and  2-10  lor 
the  width  of  shank.  Now  pivot  the  trammel  at  O  with  the  arms 
on  the  axis  FH,  then  set  from  pencil  to  minor-pin  on  the  rod,  the 
distance  O  6,  for  the  concave  side  of  mould;  now  place  the  pencil 
in  the  point  at  4,  drop  the  pins  in  the  grooves  and  fiisten  the 
uiajor-pin.  then  trace  the  curve  foi'  the  concave  .side  of  mould 
llirough  the  points  2.  0.  4.  Pepeat  the  operation  for  the  center 
and  convex  curves  of  mould. 

Tlu'  sections  of  crook  at  M  and  iVshow  the  bevel  found  in 
the  angle  at  S,  Fig.  2,  ajiplied  from  the  face  of  crook;  the  block 
j>attern  is  applied  at  right  angles  to  the  line  made  from  the  bevel, 
giving  llie  section  of  rail  and  twist  of  wreath-piece  at  the  joints. 

Figs.  4,  5  and  6.  Shows  the  construction,  of  face-mould 
for  a  quHrtcr  cylinder  on  pUin  c(n'rcs)}onding  t/}  Fig.  12,  Plate  t'), 
"■/'crc  the  learner  is  instruvicd  how  to  place  Vie  risers  in  the  cyl- 
inder. 

Fig.  4.     Shoirs  the  jdan. 

The  face  of  No.  14  rise  is  located  7^'  from  the  sjuingof  cylin- 
der and  the  face  of  No.  17  rise  is  placed  l'^''  from  the  spring  of 
cylhider;  the  radius  for  tlie  center  line  of  rail  eqnals  lOyi'^- 

The  tangents  AB  and  CB  are  at  right  angles  to  the  radial 
lines  OA  and  OC,  forming  the  square  parallelogram  OABC,  ou 
plan. 


83  Plate  11. 

Fig.  5.  Slujws  the  development  and  elevation  of  tangents, 
ulsn  the  treads  and  risers. 

Let  XX  indicate  tiie  ed^e  of  drawing  board;  make  AB  and 
BC  equal  the  tangents  AB  and  BC  on  plan.  Fig.  4;  from  the 
points  A,  B  and  C  draw  perpendiculars  to  XX  indefinite;  now 
elevate  the  risers  and  treads,  keeping  the  face  of  No.  14  rise  7^^ 
from  the  spring  line  at  A,  and  the  face  of  No.  17  rise  lU^^  to  the 
right  of  the  spring  line  at  C;  from  the  external  angle  of  No.  14 
rise,  draw  the  true  inclination  of  the  rail,  cutting  the  perpendic- 
ulars at  JD,  JE7  and  F;  from  D,  and  parallel  to  XX,  draw  DH, 
cutting  BE  &t  J;  then  HF  equals  the  height  the  wreath-piece  is 
required  to  raise;  from  J,  and  at  right  angles  to  DE,  draw  JK; 
parallel  with  BE  draw  the  half  width  of  rail  ['i''^]  cutting  the 
inclination  of  rail  at  N;  make  HL  equal  the  chord  AC,  Fig.  4. 

Bevels.  Draw  PQ  parallel  to  XX;  at  right  angles  to  XX 
draw  PR  e(iual  to  the  radius  OC,  Fig.  4;  make  P  5  equal  JK, 
draw  R  5  prolonged  to  XX  for  the  bevel  as  shown. 

Pig.  6.     Shmvs  the  fnce-monld. 

Make  AB  equal  DE,  Fig.  5;  with  A  as  a  center,  and  LF, 
Fig.  5,  for  a  radius,  draw  arc  at  C:  again,  with  S  as  a  center, 
and  BA  for  a  radius,  draw  arc  iritersecting  at  C,  join  BC;  par- 
allel to  tangent  BC  nuA  BA,  draw  tlie  radial  lines  OA  ami  OC, 
and  we  have  tl»«liarallelogram  OABC  on  the  cutting  plane,  that 
when  in  position,  '.vill  agree  with  the  parallelogram  OA.BC  on 
plan,  Fig.  4. 

Proof.  The  diagonal  BO  must  agree  with  the  diagonal  BO 
on  plan,  Fig.  4,  if  so,  the  angle  of  tangents  at  B  is  correct. 

Prolong  tangents  BA  and  BC  to  D  and  E  6'^  for  straight 
wood  on  shank;  make  joints  at  JD  and  E  at  right  angles  to  BD 
and  BE;  draw  the  diagonal  BO  for  the  direction  of  minor  axis. 
Malte  OJ" e(iual  the  radius  OC,  Fig.  4;  let  J'C  and  J 7  each  equal 
tlie  half  widtli  of  rail  [-y^];  let  A  2  and  A  3,  also  C  4  and  C  5, 
(!ach  e(iual  EN,  Fig.  5.  Parallel  to  BD  antl  BE  draw  ii  10  and 
o  11,  also  5  9  and  4  8,  for  the  width  of  shank. 

if  it  be  preferred  to  find  tlie  ijeveral  points  in  the  elliptic 
curve  and  use  a  pliable  strip  in  tracing  the  curves,  then  return  to 
j)lau,  Fig.  4;  draw  the  true  width  of  rail  [4'^j  from  the  center  O 
equally  on  each  side  of  the  center  line.  Draw  the  director  OB 
and  the  chord  AC,  forming  the  angle  at  V;  bisect  A  V  and  CV 
at  Tand  W;  from  the  points  A,  T,  V,  Wand  Cdrawordiuates 
parallel  to  the  director  OB.  cutting  the  convex,  center  and  con- 
cave curves  of  rail  at  a,  d,  h,  &c.  Now  return  to  Fig.  G;  draw 
the  diagonal  OB  and  the  chord  AC,  forming  the  ang'e  at  V: 
bisect  A  V and  CVal  Wand  T.  From  the  points  A,  T,  Wand 
C  draw  ordinates  indefinite  and  parallel  to  the  director  BO;  now 
transfer  the  points  on  the  ordinates  from  plan,  Fig.  1  to  corre- 
sponding ordinates  on  face-mould,  using  the  chord  AC  as  a  base 
line,  then  trace  the  curve  through  the  points  as  shown,  using  a 
flexible  strip. 

The  sections  at  M  and  N  show  the  bevel  found  in  the  angle 
at ."),  Fig.  5,  applieii-through  the  center  of  plauk,  so  as  to  pitch  the 
joint  at  E  up,  and  the  joint  at  D  down. 

Figs.  7,  8,  9  and  10.  Shoivs  how  to  construct  the  face- 
inoidd  for  a  quarter  cylinder  haviwj  two  wreath -pieces;  the  stv 
dent  is  shown  hoiv  to  place  the  risers  in  (he  cylinder  at  Fig.  14, 
Plate  15. 


Plate  17.  S:.: 

Fig.  7.    SJiows  the  plan. 

Draw  OA  and  OB  to  equal  12%''''  and  forming  the  right 
angle  at  O;  from  the  center  O  draw  the  center  liu«  of  rail  ACB; 
bisect  the  curve  ACB  at  C;  draw  the  ladial  line  CO;  at  right 
angles  to  the  radial  lines  CO,  AO  and  BO.  draw  lines  tangent  to 
the  curve  and  intersecting  at  D  and  F,  for  the  length  of  tan- 
gents AF,  FC,  CD  and  DB  on  plan. 

Draw  the  tangents  FA  and  DB  prolonged,  for  the  direction 
of  straight  rail;  from  C,  and  at  right  angles  to  tangent  AF  pro- 
longed draw  CH  parallel  to  tangents  CD  and  BD,  draw  BL  and 
CL  for  the  parallelogram  LCBD  on  plan.  Now  from  C  on  the 
line  of  tangents  CF,  FA  and  CD,  BD,  set  otf  half  a  tread  each 
way,  then  a  whole  tread  more,  thus  locating  the  face  of  No.  13 
and  10  risers  Q'^  from  the  spring  line  of  cylinder. 

Fig.  8.  Shoivs  the  development  and  elevation  of  tangents, 
also  the  treads  and  risers. 

Let  JCXindicate  the  edge  of  drawing  board.  Make  AF,  FC, 
CD  and  DB  equal  the  tangents  AF  FC,  CD  and  DB,  Fig.  7. 
From  the  points  A,  F,  C,  D  and  B  draw  perpendiculars  to  XX 
indefinite;  elevate  the  treads  and  risers,  keeping  the  face  of  No. 
13  and  1(>  rise  6'^  from  the  spring  lines  A  and  B;  from  the  exter- 
nal angles  of  No.  13  and  16  rise,  draw  the  inclination  of  rail,  cut- 
ting the  perpendiculars  at  H,  J,  K,  L  and  M:  from  H  and 
parallel  to  XX,  draw  HN,  cutting FJ-dt  P;  then iCiVis  the  heiuht 
the  wreath-piece  has  to  raise  from  A  to  C  on  plan,  Fig.  7.  From 
if  and  parallel  to  XX,  draw  KQ,  cutting  the  perpendicular  from  F 
at  R;  make  RS  equal  FH,  Fig.  7;  from  S  and  at  right  angles  to 
HK,  draw  SV;  make  HT  equal  the  chord  BC on  plan,  Fig  7. 

Bevels.  As  the  tangents  all  have  the  same  inclination,  only 
one  bevel  will  be  required  for  all  joints. 

Draw  ab  parallel  with  XX;  perpendicular  to  XX" draw  di 
equal  to  HC,  Fig.  7.  Make  dh  equal  SV,  Fig.  8;  draw  fh  pro- 
longed to  m;  parallel  with  XX  draw  the  half  width  of  rail 
cutting  mf  at  y. 

Fig.  9.  Shows  the  facc-iaotdd,  the  trammel  or  straiQht 
edgehcing  used  to  draio  the  cUlptie  curves. 

Make  AJP  equal  HJ"in  elevation,  Fig.  8;  with  A  as  a  center, 
and  TQ,  Fig.  8,  for  a  radius,  draw  arc  at  C;  again  with  JPas  a 
center  and  FA  for  a  radius,  draw  arc  intersecting  at  C.  .Join 
FC  parallel  with  FC  and  FA,  draw  AL  and  CL  for  the  paral- 
lelogram LAFC  on  the  cutting  plane. 

Proof.  The  diagonal  J/J" must  equal  the  diagonal  LD,  Fig. 
7.     If  so,  the  angle  at  F  is  correct. 

Trolong  the  diagonal  FL  to  O  equal  to  DO,  Fig.  7,  draw  the 
radial  lines  OC  and  OA.  Make  OP  equal  the  radius  OA  on  plan, 
Fig.  7;  prolong  tangent  JPA,  6'^  to  T  for  length  of  shank;  make 
joints  at  rand  Cat  right  angles  to  FT  and  FC.  Let  C2,  and 
C3,  also  Ti  and  T5  equal  yni.  Fig.  S;  from  4  and  5  draw  lines 
parallel  to  TA,  intersecting  the  radial  line  OA  produced  at  7  and 
(5;  let  P  8  and  P  9  each  equal  the  half  >vidth  of  rail  [2^^].  Now 
pivot  the  trammel  in  the  point  at  O  with  the  arms  at  right  angles 
to  OP;  for  the  convex  curve,  set  from  pencil  to  minor-pin  on  rod, 
the  distance  0  9,  [14M^^].  tlien  place  the  pencil  in  the  point  at  7. 
and  shift  the  major-pin  until  l)Oth  drop  into  the  grooves,  then 
fasten  the  major-pin  and  trace  the  curve  through  the  points  7,  9, 
3,  for  the  convex  curve  of  mould;  proceed  in  like  manner  to  trace 
the  concave  curve  through  the  points  6,  8,  2,  for  which  set  the 
minor-pin  to  O  8,  or  10%^^  for  the  semi-minor  axis,  and  proceed 
as  above.  '  r- 


84  PI.ATK   17. 

The  sectious  Jif  and  iVshow  the  bevels  applied  from  the  face 
of  crook  through  the  center  of  plank,  so  as  to  pitch  the  shank 
down,  and  the  center  joint  up. 

Fig.  10.  Shows  the  face-mould  drawn  by  the  use  of  ordinates;  less 
space  being  retiuired  than  by  the  trammel;  in  many  cases  the  ordi- 
nates are  to  be  preferred,  as  in  large  sweeps  where  the  rooru  required 
for  the  trammel  is  limited;  it  will  be  seen  in  this  way  any  number  of 
ordinates  can  be  used. 

On  plan,  Fig.  7,  set  off  the  half  width  of  rail  [2^^]  on  each 
side  of  the  center  line  of  rail  ACB.  Draw  Cy  indefinite  ; 
draw  the  chord  BC  prolonged ;  perpendicular  to  BC  as  a 
center,  and  TQ,  Fig.  8,  for  a  radius,  draw  arc  cutting  Cy  at 
2;  draw  B  2  prolonged;  draw  any  number  of  ordinates  parallel 
with  the  director  LD  to  cut  the  curves  of  rail,  and  also  the  chord 
.BC  on  plan,  and  prolonged  to  intersect  J3  2  at  3,  4,  5  and  6,  &c. 

Fig.  10.     Shoivs  the  fncc^noiild. 

The  parallelogram  LCDB  is  laid  off  in  the  same  manner  as 
at  Fig.  9,  and  need  not  be  repeated. 

Prolong  tangent  DB.  ^''  to  T;  make  joints  at  T  and  C  at 
right  angles  to  -DT  and  DC;  draw  the  chord  BC  prolonged,  nuike 
BCequal  B  2,  Fig.  T.  Now  transfer  the  spaces  6  5,  .5  4,  4  2  and  2  3,  on 
plan,  Fig.  7,  to  the  chord  BC,  Fig.  10,  now  draw  ordinates  through 
the  points  3,  B,  4,  5.  6,  5,  4,  C  and  3,  parallel  to  the  director  BL 
indefluite;  then  transfer  points  en  the  ordinates  on  plan.  Fig.  7. 
to  corresponding  ordinates  on  face-mould,  using  the  chords  BC 
as  a  base  line;  now  through  the  points  trace  the  curves  for  the 
face-mould. 

The  sections  at  Jif  and  N  show  the  bevels  applied  reverse  to 
those  at  Fig.  9;  at  section  iVthe  bevel  is  applied  so  as  to  pitch  the 
shank  up,  and  at  M  the  bevel  is  shown  applied  so  as  to  pitch  the 
joint  at  Cdown. 

Figs.  11,  12  and  13.  Shoirs  the  elevation,  ground  plan 
and  face-mould  for  a  *•  turnout"  starting  from  a  newel,  ihc 
V08t  is  8^^X8^^,  balusters  2"y:2",  rail  4"yC2}i'',  the  rise  and 
tread  is  l"y^lO", 

Fig.  11.     Shows  tlie  elevation. 

Begin  by  elevating  two  or  three  risers  and  treads  from  the 
base  line  XX,  as  No.  1,  2  and  3  rise.  From  the  top  of  No.  1 
step  set  up  to  the  underside  of  rail  the  difference  [.5^^]  that  the 
newel  post  is  longer  than  a  short  baluster  and  IH^^  more,  making 
dH^^  from  the  top  of  No.  1  step  to  the  ceuter  of  rail  as  shown.  At 
this  height  draw  the  center  of  level  rail  DH  parallel  with  XX; 
from  the  face  of  No.  2  and  3  rise  set  off  the  ceuter  of  short  balus- 
ter 00,  through  00,  draw  the  inclination  of  the  underside  of  rail; 
parallel  with  00  draw  the  center  of  inclining  rail  to  intersect  the 
center  of  level  rail  at  F;  from  F  let  fall  the  perpendicular  inter- 
secting the  base  line  XX  at  B. 

Now  commence  the  plan,  Fig.  12.  Draw  YT indefinite,  to 
indicate  the  center  line  of  rail  or  center  of  baluster  on  plan.  Set 
off  No,  1,  2,  3  rise  and  the  point  S  to  correspond  with  Fig.  11. 
Set  the  ceuter  of  newel  at  H  on  line  with  the  face  of  No.  1  rise. 
and  in  this  case  let  the  side  of  newel  be  on  line  with  the  center  of 
baluster,  and  as  the  newel  is  8'^  in  diameter,  the  center  of  newel 
will  be  out  4^''  from  the  center  of  baluster.  For  small  halls  this 
is  the  usual  way  to  locate  the  newel  when  a  turnout  wreath-piece 
is  required;  the  newel  may  be  set  on  an  angle,  or  square  with  the 
rise,  or  may  be  set  further  out  or  in,  as  the  stairbuilder  may  desire; 
the  location  is  a  matter  of  taste  and  couvenieuce;  the  piinciple  in 
getting  the  face-mould  is  the  same. 


Pi- ATE  17.  sr> 

Fi-om  the  center  of  uewel  at  H  ^ll•a^^•  HB,  draw  the  verge  of 
cap  cutting  HB  at  2;  from  3  set  oil'  the  halt  width  of  rail  [3^^]  to 
the  point  of  miter  at  A;  make  BC  equal  BA  for  the  tangents  on 
plan.  From  the  points  A  and  C  draw  the  radial  lines  at  right 
angles  to  the  tangents  AB  and  CB;  from  the  converging  point 
(not  shown  on  plan)  draw  the  curves  of  rail  on  plan.  The  face  of 
Xo.  o  rise  is  ^}i^'  from  the  spring  of  cylinder;  draw  AO  and  CO 
jiarallel  with  the  tangents  BC  and  BA  for  the  parallelogram 
0 ABC  on  plan;  from  A  and  square  to  YT  draw  Ai). 

Now  return  to  elevation,  Fig.  11,  make  BA  and  BC  each 
equal  tangents  BA  and  SC  on  plan,  Fig.  13,  from  the  points  A 
and  C,  draw  perpendiculars  to  XX,  cutting  the  center  of  level 
rail  at  D  and  the  inclining  rail  at  G;  prolong  jDJ'to  intersect  CG 
at  H,  then  HG  is  the  hcifjlit  the  wreath-piece  is  required  to  raise 
in  the  curve.  Make  HJ  equal  the  chord  AC,  Fig.  12;  lat  HK 
equal  the  diagonal  BO,  Fig.  12.  jNIake  JX  equal  JBJD  on  plan, 
¥\g.  12;  from  L  and  at  right  angles  to  G^ J*  prolonged,  draw  LM. 

Bevels.  Draw  dP  parallel  to  XX:  draw  Pq  perpendicular 
to  XX  and  equal  to  AD,  Fig.  12;  make  jjr  equal  to  LM,  Fig.  11, 
also  make  ps  equal  the  height  HG,  Fig.  11,  draw  qr  and 
qs  prolonged  to  edge  of  board  for  convenience  when  setting  the 
bevels.  Parallel  with  np  draw  the  half  width  of  rail  [2^'],  cut- 
ling  rq  at  o,  and  also  sq  at  4. 

^  Fig.  13.    Shows  the  face-mould. 

Let  CB  equal  FG  in  elevation.  Fig.  11.  With  C  as  a  center 
and  JG,  Fig.  11,  for  a  radius,  draw  arc  at  A;  again,  with  .B  as  a 
center  and  tangent  BA,  Fig.  12,  for  a  radius,  draw  arc  intersect- 
ing at  A,  join  BA;  draw  AO  and  CO  parallel  with  tangents  BC 
and  BA  for  the  parallelogram  OABC  on  the  cutting  plane. 

Proof.  The  diagonal  OB  must  equal  the  distance  KG,  Fig- 
11.     If  so,  the  angle  of  tangents  at  B  is  correct. 

I'rolong  tangent  BC,  T'^  to  25  for  length  of  shank,  make  joints 
at  A  and  D  at  right  angles  to  AB  and  BD;  make  A  2  and  A  o 
each  e(iual  S  4,  Fig.  11,  make  D4  and  1?  5  each  equal  rC,  Fig. 
1 1 :  prolong  the  joint  line  at  A  indelinite,  also  prolong  the  diagonal 
BO  to  intersect  the  joint  line  at  L,  from  L,  through  C,  draw  tJie 
radial  line  for  the  point  of  tangency  or  connection  of  straight 
with  the  circular  part.  From  the  points  4  and  5,  draw  lines  par- 
allel with  BD  to  cut  the  radial  line  LC  produced  at  6  and  7;  now 
connect  the  points  2,  6  and  3,  7  with  the  curves  as  shown,  using 
a  flexible  strip,  being  careful  to  draw  the  curves  to  tangent  the 
straight  part  at  points  6  and  7;  also  see  that  the  curves  connect 
tlie  joint  A  about  square  to  the  joint.  The  curves  may  be  drawn 
with  the  traunnel  centered  at  L,  with  the  arms  resting  on  the 
semi-major  axis  LA ;  but  to  use  the  trammel  in  this  case  would  be 
tdo  unhandy  and  attended  with  too  much  loss  of  time.  Face- 
moulds  of  tliis  kind  the  practical  stairbuilder  can  draw  the  curves 
l>y  using  a  pliable  strip  thinned  down  at  one  end. 

'i'he  sections  of  crook  at  M  and  N  show  the  bevels  applied 
from  the  face  of  plank;  the  bevel  found  in  the  angle  at  S,  Fig.  11, 
is  sliown  applied  at  section  Jf  and  the  bevel  shoMii  at  the  angle 
r.  Fig.  1 1,  is  applied  at  section  N.  Observe  they  do  not  cross  the 
tangents  in  their  application. 

Fig.  14.  Shows  the  same  face-mould  draivn  ^vith  less  lines, 
hut  not  so  correct  as  shonm  at  Fig.  13. 

'i"o  find  the  angle  of  tangents  at  B  lay  down  the  steel  square 
and  draw  the  right  angle  ASD  indefinite;  make jS.B,  BCand  CD 
equal  MF,  FG  and  GV,  Fig.  11.    AYith  B  as  a  center  ami  tan- 


86  Plate  18. 

gent  AB,  Fig.  12,  for  a  radms,  draw  arc  intersecting  SA  at  A, 
connect  BA,  thus  establisliing  the  angle  of  tangents  at  B. 

Proof.  The  distance  AC  must  equal  JG,  Fig.  11.  Make 
joints  at  A  and  D  at  right  angles  to  BA  and  BD;  let  A  2  and  A  3 
each  equal  S  4,  Fig.  11,  also  let  D  4  and  D  .5  equal  rZ,  Fig.  11; 
from  4  and  5  draw  lines  indefinite,  and  parallel  to  SD;  now  draw 
the  concave  and  convex  curves  of  mould,  using  a  pliable  strip 
tapered  at  one  end.  Connect  A  4  on  plan.  Fig.  12,  for  the  miter 
on  plan;  make  3  6  equal  3  4,  Fig.  12,  draw  A  6  for  the  miter  on 
face-mould. 

Any  face-mould  may  be  dra^vn  in  this  way,  if  the  stairbiiilder 
prefers;  by  increasing  the  number  of  lines  a  third  point  in  tlie  curve 
may  be  found  on  the  diagonal  OB  prolonged,  Fig.  13,  to  which  Ave  will 
refer  at  another  time. 

The  bevels  as  applied  at  sections  M  and  JV  are  the  same  and 
applied  in  lilce  manner  as  those  shown  at  Fig.  13. 

At  Fig.  14,  if  the  points  of  tangency,  or  connection  of  the  straight 
with  the  circular  part  is  required,  then  draw  the  proportional  line 
AC;  from  2  and  3  and  parallel  to  AC,  draw  lines  to  intersect  the  par- 
allel lines  from  4  and  5  at  6  and  7;  then  the  points  at  G  and  7  show  the 
connection  of  the  straight  with  the  circular  part  without  extending 
the  long  lines  as  at  Fig.  13. 


PLATE  18. 

Fig.  1.  Exhibits  the  plan  of  n  hrtlf  pace  irinding  '^  doq- 
IcrirjccV  stair-case.  Hall  b.S"  wide,  the  center  of  rail  being  the 
center  of  liall,  and  so  of  all  succeeding  fliijhts  composing  the 
sta  ircase. 

The  rail  starts  at  the  first  newel  and  terminates  at  the  second, 
and  from  second  to  the  newel  at  the  landing  finishing  with  a  ramp 
and  knee  against  the  newel;  if  instead  of  winders  there  be  a 
jilatfonn,  then  the  first  length  would  intersect  the  lower  edge  of 
outer  string  on  the  return  flight,  miter  and  finish  down  the  lower 
edge  of  string  and  the  triangular  space  filled  with  balusters  of  odd 
lengths  or  ornamental  panel  work.  On  account  of  room  winders 
occupy  the  half  pace  in  this  case  instead  of  a  platfonn.  The 
newel  at  the  winders  is  placed  in  the  center  of  ball  2''  7)4^^  from 
wall  to  center  of  post.  The  space  is  divided  off  on  the  semi-circle 
into  six  winders;  the  risers  and  tread  part  of  steps  should  be 
housed  into  the  post,  also  the  nosings  that  join  the  post  at  right 
angles  to  its  face. 

The  manner  of  getting  out  winders  for  tlais  kind  of  stairs  is 
explained  at  Plate  20. 

Fig.  2.  Shoxvs  2>lan  of  quarter  pace  winding  stairs  of  13 
risers. 

The  flyers  to  the  winders  is  open  on  one  side  and  the  flyers 
above  the  winders  is  closed  between  partitions;  in  the  quarter  pace 
four  winders  are  used  divided  off  equally  on  the  quarter  circle. 
The  corner  is  allowed  to  be  cased  up  so  as  to  receive  the  risers  and 
steps  at  the  narrow  end.  The  flyers  or  straight  steps,  Nos.  1,2,  3, 9, 
10,  11,  12  and  1.3  are  housed  into  wall  strings  on  the  right  and  left 
hand  side.  I'lie  first  three  steps  are  sided  up  on  the  right  with 
narrow  flooring  and  cut  off  hand-rail  high  and  capped,  the  siding 
is  ploughed  into  the  post  }4''\  In  first-class  houses  No.  4  and  9 
steps  may  be  diminished  at  A,  so  as  to  increase  the  width  of  wind- 
ers at  the  narrow  eiuls.  the  corner  may  be  rounded  and  the  string 
carried  around,  and  the  steps  and  risers  housed  into  the  string, 


Plate  18  87 

thus  taking  away  the  sharp  angle  of  the  winders  at  the  narrow 
ends,  and  giving  a  better  finish  to  the  string  and  wall  rail,  if  used. 

Fig.  3.  Shows  iJlun  of  a  quarter  pace  booc  stairs  containing 
12  rl'^ers. 

[Scale  >4''^=1  foot].  The  stairs  are  planned  so  as  to  admit 
light  at  the  quarter  pace,  a  window  should  not  be  neglected  in 
these  close  stairs,  either  on  the  side,  or  as  a  skylight  in  the  roof, 
for  both  light  aud  ventilation.  The  construction  is  the  same  as 
explained  for  Fig.  1,  Plate  19. 

Fig.  4.  Sfwws  plan  of  an  outside  steps  at  the  front  door. 
[Scale  ^'"=1  foot]. 

The  height  at  a  point  3'  S^^  from  the  building  to  the  level  witli 
the  top  of  the  front  door  sill  equals  3^  9, '.<'",  which  being  divided 
into  seven  equal  parts,  will  allow  6K^^  for  the  height  of  each  rise; 
and  as  we  are  not  limited  to  the  run,  we  may  use  Blondel's  form- 
ula for  the  relative  width  of  tread  to  the  height  of  rise. 

Rule.  From  the  constant  24'''  take  twice  the  height  of  rise, 
l-j4''_6>^'^X2=ll''],  for  the  tread,  equals  11^'  for  the  breadth 
of  tread;  this  gives  an  easy  grade  to  the  steps,  6)^'^  rise,  by  ll'" 
tread.  The  breadth  of  steps  from  wall  to  outer  edge  of  nosing  is 
:'>'  5",  the  landing  should  drop  down  one  rise  below  the  door  sill, 
then  there  will  be  6  risers  as  shown  to  the  platform.  A  stone  at 
jB  is  bedded  in  the  pavement  to  start  the  first  rise  off,  sometimes 
the  first  step  is  of  stone,  which  is  better,  as  the  wood  work  is  kept 
higher  off  the  ground. 

Fig.  5.    Shows  the  elevation. 

The  steps  are  of  white  pine,  Ui"'  thick,  the  nosings  are 
returned  on  the  front  string  over  plain  brackets;  tbe  balusters  are 
shown  dovetailed  into  the  steps;  the  newel  post  is  shown  anchored 
into  the  stone,  having  an  "upset"  bolt  leaded  into  the  stone,  and 
extended  up  into  the  post  with  a  nut  at  the  end  as  shown  at  A. 

For  the  full  width  of  steps,  take  the  tread  If^  plus  the  pro- 
it'Ctiou  of  nosing  [IK''^]  equals  l'33'i'^  plus  ^s^^  for  tongue  into 
tlie  rise  at  the  internal  angle,  equals,  [ll^'+l>a'^-K^|''''=ia%^'] 
fur  the  full  width  of  steps  Vi}^^^. 

For  all  outside  steps,  each  step  should  have  a  wash  of  ^i^^  in 
every  12''^,  so  as  to  allow  the  water  to  run  off;  this  is  not  too  much, 
for  the  step  is  liable  to  turn  up  at  the  nosing,  and  the  middle  of 
.>tep  to  become  dished  and  hold  the  water  after  a  rain;  the  reason 
that  the  steps  become  caped,  arises  from  the  dampness  under- 
neath, aud  for  this  reason  the  steps  and  risers  should  have  a 
heavy  coat  of  paint  on  the  underside,  before  fixing  in  place,  so  as 
to  prevent  the  wood  from  taking  the  moisture. 

Then  after  the  pitchboard  is  made  in  the  usual  way  GJ^" 
by  If;  take  olf  on  the  tread  side  of  pitchboard  J4'^  at  the  right 
angle  and  nothing  at  the  point,  this  will  give  each  tread  the  re- 
quired wash,  and  reduce  the  rise  to  5%'''' by  11^''  on  the  cut  out  of 
"horse"  or  string. 

How  to  take  the  lengths  of  rail  so  as  to  cut  aud  make  all 
joints  at  the  l)ench.  Plumb  down  the  face  of  No*  2  and  No.  6  rise 
on  the  face  of  string  as  2  J3  and  6  C,  then  the  distance  BC, 
[I'.Sj-.;'']  taken  parallel  with  the  lower  edge  of  string,  is  the 
length  for  the  inclining  rail;  then  measure  from  the  face  of  land- 
ing rise,  [No.  6]  to  the  center  of  baluster  on  the  corner  [.5''.2'''] 
then  take  the  distance  HJ  on  plan,  from  center  of  baluster  to 
wall. 


88  Plate  18 

Rnviiuj  the  lengths  of  rail,  how  to  make  the  easinri  patterns, 
and  mark  the  points  B  and  C,  on  the  patterns,  so  that  the  rail 
will  he  the  required  height  at  the  newel,  and  also  on  tlie  level,  and 
cut  all  joints  at  the  bench. 

First  witli  the  pitchboard  lay  off  a  few  steps  and  risers  as  1,  2 
and  3,  from  the  edge  of  a  board,  say  12'^  wide;  draw  the  under 
side  of  rail  through  the  center  of  baluster  kk;  parallel  to  kk 
draw  2121  for  the  center  of  rail.  Now  make  ma  equal  half  a  rise, 
[3Ji^^]  and  draw  the  under  side  of  rail  up;  then  transfer  the 
angle  apk  to  the  board  from  which  the  pattern  is  to  be  made,  and 
ease  off  the  angle  with  the  easing  pattern  for  the  under  side  of 
rail;  now  gauge  for  the  width  of  pattern;  then  lay  the  pattern 
down  on  the  drawing  so  the  lines  kp  and  ap  will  agree  witli 
same  lines  on  the  pattern;  then  mark  the  face  of  No.  6  rise  across 
the  pattern  to  intersect  the  center  line  nn  at  r. 

For  the  easement  at  the  newel,  decide  upon  tiie  length  of 
short  baluster  from  top  of  steps  to  the  under  side  of  rail  at  the 
center  of  baluster,  say,  I'.ll'^.  Also  decide  upon  how  much 
higher  the  newel  is  than  a  short  baluster  measuring  from  tiie  top 
of  step  to  the  under  side  of  rail,  say  !'/\  Then  make  FS  equal 
5'',  and  draw  the  dotted  line  ts  at  right  angles  to  the  rise;  then 
transfer  the  angle  tsk  to  tlie  board  from  which  the  pattern  is  to 
be  made,  and  ease  the  angle  to  suit;  then  dress  off  to  the  curve, 
and  gauge  to  the  width  required  for  the  depth  of  rail;  now  lay  the 
pattern  over  the  drawing  to  the  lints  ts  and  sk  so  tiiat  they  will 
agree  with  same  lines  on  pattern,  then  mark  the  face  of  No.  2 
rise  cutting  the  center  line  n2l  at  x;  also  mark  the  line  of  newel 
post.  Then  the  distance  x^r  eriuals  the  distance  BCou  the  string, 
and  is  etiual  to  the  length  to  cut  the  straight  rail  on  the  rake,  le^s 
the  straight  wood  on  the  patterns,  as  shown  on  rail  in  elevation. 

Now  the  post  is  to  be  "/'longer  than  a  short  Itahistcrl  1'.  ll"] 
equals  [V.  W"^^  h"^^l' .  \"\  frinu  the  t<q)  of  step  to  underside  of 
rail  2'.  ^",  or  from  the  lop  of  stone  lo  underside  of  rail  ^%" 
more,  or  3'.  ^M". 

Lines  are  shown  converging  at  H.  from'vhich  the  curve  of 
easement  may  be  drawn. 

Fig.  6.  Shoirs  plan,  of  nn  oiilnlde.  cellar  fiiijht  of  stairs 
under  a,  store-room.     (>^cnle  ^i''^=l  foot]. 

"j  The  opening  is  4'.  0''  wide,  and  the  run  for  the  steps  is  4'. 
6'".  The  height  from  cellar  floor  to  kvel  with  the  top  of  stone 
sill  at  pavement  is  6'.  3". 

Fig.  7.     Shoujx  tiic  clenaliiin. 

The  height  (j'.  S^'beingdividiwl  iuto  nine  risers  [G.'  3^^X12'''=^ 
7:,  H9=:8/e  full]  equals  8v'„''  full  fen-  the  height  of  rise,  the  njn 
being  divided  by  i).  [4'.  0'';^  12''=.54^-y  ^-G''J  equals  0'^  for 
each  tread. 

Right  here  let  it  be  observed  we  have  divided  tiie  run  into  the  same 
ituuilier  of  parts  as  tlie  lieij;lit  foi-  tiie  risers,  and  iir>t  madu  tlie  spac<? 
for  Hie  treads  one  less  as  in  r)tiii;f  cases,  for  (iiis  reason,  if  we  had 
Inlceii  (lie  wliole  spiice  and  oinde  the  division  f)iie  less  tlien  tlie  tnn'se 
and  skid  piece  B  would  have  extended  out  lieyond  tlic  wall  at  A 
too  fa  r. 

The  steps  should  be  made  from  S'' oak,  housed  into  oak  liorses 
and  well  spiked  together  and  made,  measuring  l)etween  thestrings 
about  12-'''  narrower  than  the  w  idth  of  opening.  This  allows  G'" 
on  each  side  for  the  .skids  SS,  which  i)roject  abov(!  the  edge  o! 
steps  so  that  in  sliding  heavy  boxes  down  tliey  will  i)rolect  the 
steps.  These  skids  are  si)iked  to  the  horses  and  also  into  a  timber 
placed  between  the  horse  and  the  wall:  D.  D,  D,  shows  the  hous- 
ini,'^.     Tlie  horse  is  12"  wide.. 


Plate  19.  89 

The  opening  to  the  pavement  is  closed  witli  iron  doors  resting 
on  a  heavy  iron  bar  shown  at  F.  These  doors,  after  folding  down 
on  this  bar,  are  locked  by  two  other  iron  doors  folding  in  a  vertical 
position,  and  are  held  in  place  by  the  bar  shown  at  H. 

Fig.  8.  Slioivs  the  elevation  of  a  step-ladder  iised  to  get 
into  the  "cock-loft,"  or  ''^  blind-c/arret,"  and  also  for  an  exittotfw 
■roof  in  case  of  fire,  or  any  repairs  that  may  be  tiecded. 

The  height  from  floor  to  underside  of  rafters  is  IV.  0^^;  the 
run  is  4^  0^^;  the  height  to  garret  floor  is  9''  C.  The  whole  height 
we  will  divide  into  eleven  risers  at  12^^  each,  that  will  allow  No. 
9  tread  to  come  level  with  the  attic  joist.  The  whole  run  equals 
i'.  0^^  or  48'^  The  tread  at  the  top  of  ladder  is  9^^^  wide,  ^^  hicli 
will  leave  i\  0^'  minus  9)^^^  equals  3''.  2}4^^,  which  being  divided 
into  eleven  parts  equals  3>^^^  for  each  tread,  and  also  3}4^^  more 
for  the  foot  of  ladder  at  A  ;  also  the  sides  of  ladder  should  be 
at  least  IJi^''  thick  and  8'^  wide. 

In  this  case  it  will  not  be  necessary  to  make  a  pitchboard 
take  the  steel  square  and  with  12''''  on  the  blade  and  SK ^''  on  the 
tongue,  draw  the  tread  J)F  from  the  tongue ;  and  the  rise  FJ 
from  the  blade,  continue  the  line  DF  to  H,  and  with  tht^ 
compasses  take  the  hypothenuse  DJ,  and  space  off  eleven  spaces 
on  the  edge  of  horse  AX  as  J  2,  2  3.  Then  place  the  two  horses 
together  and  transfer  the  divisions;  then  set  the  bevel  to  the  angle 
JDH,  and  with  it  lay  off  the  steps,  also  their  thickness  and  gain 
in  the  horses  )4."'  At  two  or  three  intervals  tenon  the  step 
through  the  horses  and  glue  and  wedge  the  tenons  F  and  K.  The 
ladder  may  be  26^''  wide.  At  i  a  trap  door  is  shown  leading  into 
the  garret  and  the  scuttle  M  in  the  roof;  the  door  in  the  roof 
should  be  carefully  covered  with  tin  and  the  curb  around  raised 
above  the  roof  with  flashings  carried  up  and  turned  over  the  upper 
edge  of  curb;  also  the  tinning  on  the  door  extended  down  to 
the  roof  to  answer  for  cap  flashing;  if  the  tinning  be  done  in  this 
way  there  will  be  no  leaking;  two  hooks  and  steeples  are  required 
to  fasten  and  keep  the  door  in  place.  At  C  is  shown  a  light  rail- 
ing for  hand-holt. 

For  outside  steps,  sap  ■wood  should  not  be  used,  a  sound  knot  is  to 
be  preferred:  if  tlie  heart  side  be  turned  downtlie  stop  will  wear  lontrer 
for  exposed  work;  if  inside  then  the  heart  side  will  be  more  durable, 
taut  is  more  difticult  to  work  smooth  than  the  side  nearest  to  the  bark. 
Oak  is  to  be  preferred  for  outside  steps;  white  pine  is  better  than 
yellow  pine;  all  outside  steps  sliould  1)0  constructed  so  as  to  admit  a 
free  circulation  of  air,  and  painted  luiderneath  as  well  as  above  to 
protect  them  from  the  dampness.  The  following  is  a  very  good  pro- 
portion for  the  thickness  to  length  of  steps. 

Steps  3'.  0"  long,  l^^"  thick.  Steps  C.  0"  long,  IV^"  thick. 

Steps  3'.  fi"  long,  1  3-16"  thick.  Steps  6'.  6"  long,  \%"  thick. 

Steps  4'.  0"  long,  l>.i"  thick.  Steps  7'.  0"  long,  \\"  thick. 

Steps  4'.  G"  long,  1  5-16"  thick.  Steps  7.  6"  long,  I's"  thick. 

Steps  .V.  0"  long,  l^g"  thick.  Steps  8'.  0"  long,  T  thick. 

Steps  5',  6"  long.  1  7-16"  thick. 


PLATE  19. 


Plate  19.  [Scale,  \i"=\  foot].  S/ioics  various  29?«7is  of 
close  or  box  stairs,  built  either  between  two  walls  or  a  wall  on  the 
one  side  and  lined  up  on  the  other  with  flooring.  In  first-class 
box  stairs  a  wall  rail  is  secured  to  the  loall  by  "■holdr-fasts,"  and 
is  alloived  to  project  clear  of  the  ivall  not  less  than  one  and  a 
half  [IM'^]  inches. 


90  PLATE  19. 

Fig.  1.  Shoivs  the  plan  of  a  flir/ht  of  box  stairs  having  a 
straight  run  of  16  risers,  landing  on  a  level  with  the  flow  in  the 
next  story.    How  to  proceed  and  construct  the  same. 

First  take  the  height  of  story  from  top  to  top  of  joist,  [10''.2''''] 
as  shown  in  elevation,  Fig.  2;  then  tlie  widtli  of  opening,  [3^.0^^], 
then  the  hoj'izontal  distance  from  the  face  of  first  rise  to  plumb 
Avith  the  last  rise.     [ll^S^^J. 

Having  taken  the  measures,  then  proceed  to  layoff  the  risers. 
Provide  a  story  rod  made  from  pine  IH^^  square,  and  13  or  10 
feet  long,  dressed  np  square,  and  for  convenience,  mark  off  one 
side  into  feet  and  number  the  same;  have  the  rod  kept  in  a  rack 
for  this  special  purpose. 

Now  set  oif  on  the  rod  the  height  of  story,*  Fig.  2,  equal  to 
lO'',  3^^,  then  with  a  large  pair  of  dividers,  space  off  the  height 
into  16  parts,  which  will  equal  "7%^^  each,  and  are  termed  the 
"risers";  the  number  of  full  steps  will  always  be  one  less;  there- 
fore in  this  case  there  will  be  15  full  steps  required. 

Now  the  horizontal  distance  including  the  landing  equals 
14'',  3^^.  We  must  allow  for  the  quarter  pace  at  the  landing  at 
least  3'',  C^,  leaving  for  the  run  the  horizontal  distance  11^,  3^^. 
which  equals  135''^  to  be  divided  into  1.5  equal  parts.  fl35-=-15^^ 
=9^'']  equals  9^''  for  each  division  termed  the  "  tread";  if  including 
the  projecting  nosing,  each  division  is  then  termed  the  "  step." 

Now  we  have  the  pitch  or  cut  out  on  horse  7^  rise  by  9'^ 
tread.  The  next  will  be  to  make  a  pitchboard,  have  the  grain  to 
run  parallel  with  the  hypothenuse  or  long  side;  see  that  it  is  exact 
to  the  rise  on  the  rod  as  shown  at  A  in  elevation,  also  to  the  tread 
as  shown  at  B  on  plan.  Fig.  l;if  there  are  several  flights  of  stairs 
to  the  same  pitch  then  make  the  pitchboard  from  some  hard  wood. 
Two  wall  strings  will  be  required,  the  one  on  the  left  ascending 
will  require  an  easing  at  the  starting  and  also  at  the  landing,  the 
string  on  the  right  will  not  require  any  easing,  as  the  room  will 
not  admit  of  any. 

Now  select  .the  planks  for  the  wall  strings  about  13'^  wide; 
allow  the  external  angle  Cof  rise  and  tread  to  extend  down  from 
the  top  edge  of  string  from  ?/^  to  4'^,  tlien  the  breadth  of  pitch- 
board  more,  say  to  the  internal  angle  of  tread  and  rise  marked 
D;  through  the  point  marked  D,  run  a  gauge  line  3  3  from  the 
edge  of  string;  then  take  the  pitchboard  and  turn  the  hypothe- 
nuse or  long  side  down  on  a  flat  surface,  and  with  a  well  pointed 
knife-blade  mark  the  extreme  points  of  pitchboard,  (see  Fig.  7, 
Plate  30)  take  the  space  thus  marked  otf,  with  a  large  pair 
of  dividers  carefully;  and  step  off  on  the  gauge  line  the  required 
number  of  risers  and  treads.  Then  apply  the  pitchboard  as  at 
Jf,  with  the  long  edge  of  board  to  the  gauge  line,  and  with  a 
knife  blade  mark  the  rise  and  tread  as  indicated  in  elevation. 
After  all  the  risers  and  treads  have  been  marked  ofl;  apply  the 
J  lousing  pattern  and  mark  the  honsings  for  the  rise,  tread  and 
wedge-roomf  with  the  pencil.  Now  with  a  square  mark  all  the  in- 
ternal angles  of  risers  and  treads  out  on  the  edge  of  string  as  at  3,  3, 
3;  then  turn  the  face  side  of  No.  3  string  doAvn  on  No.  1  and 
transfer  the  divisions.  Carry  the  points  over  to  the  gauge  line 
that  has  already  bten  run  on  No.  3  board  and  apply  the  pitch- 
board  and  housing  pattern  as  before;  both  strings  will  now  agree. 

"  *The  stair-builder's  height  of  .story  is  from  top  to  top  of  floors;  the 
carpenter's  height  of  story  is  in  the  clear  from  floor  to  ceiling.     ^ 

+The  wedges  aie  u.sually  %  at  the  thick  end  and  tapered  to  a U"  at 
the  thin  end  in  a  distance  of  10".  For  all  lengths  the  taper  should  be 
the  same. 


Platk  19.  91 

Glue  on  at  4  the  triangular  piece  to  form  the  easing  at  the 
lower  end.  Measure  up  from  the  floor  line  the  height  of 
base  [7^^],  draw  lines  with  pencil  parallel  with  the  floor  line  as 
shown.  Then  take  the  easing  pattern,  Fig.  3,  and  apply  the  shank 
CD,  to  the  upper  edge  of  string  and  tangent  the  level  line  4  5,  in 
elevation,  and  draw  the  full  easing  as  shown.  Do  the  same  at  the 
lower  end,  clean  off  the  surplus  wood  and  kerf  in  at  each  end  K''''; 
so  as  to  make  a  clean  joint  at  the  joining  of  the  base.  The  rule 
for  height  of  base,  inclvddng  the  mouldinfj  relative  to  the  height 
of  story  is  one  inch  for  every  foot  high  the  story  is  in  the  clear. 

The  easing  pattern  shown  at  Fig.  3  is  drawn  M^^  to  the  foot, 
the  arc  ABC  has  for  its  radius  19^^,  and  is  made  from  X^^  stufl", 
For  all  full  easements  starting  and  landing,  the  stair-builder  will 
find  this  pattern  very  usefnl. 

Housing  in  the  Wall  String.  Where  the  stair-builder  has 
steam  power,  there  is  nothing  to  equal  Mr.  Parry's  Router  for 
gaining  in  the  Avail  strings.  Much  time  is  saved  over  the  old 
method,  for  with  its  use,  the  gauge  line  nor  any  laying  out  with 
the  pitchboard  is  required  on  the  wall  string  to  be  housed,  all  that 
is  necessary  to  be  done  is  to  set  the  dividers  to  the  hypothenuse 
of  pitchboard,  and  mark  the  divisions  3,  3,  3,  &c.,  along  the  edge 
of  string,  then  each  division  serves  as  a  guide  to  shift  the  string 
on  the  machine. 

If  the  work  is  to  be  done  by  hand  labor,  the  speediest  way  is 
to  bore  two  or  three  holes  in  each  tread  and  rise  at  the  external 
angle  C,  in  elevation.  Then  mortice  and  clean  out  to  the  required 
depth,  and  cut  down  to  the  depth  of  housing  with  a  "back-saw," 
having  a  guide  fastened  to  each  side  of  the  saw  to  gauge  the  depth 
(if  the  housing;  then  clean  out  with  a  chisel,  or  a  "hand-roiiter," 
that  is  sold  in  most  of  the  hardware  stores  for  that  purpose.* 

Stairs  of  this  description  having  a  straight  run  of  15  or  10 
risers  may  be  put  together  in  the  shop  and  set  up  in  the  building; 
the  stair-builder  in  that  case  must  be  careful  in  taking  the  dimen- 
sions, also  see  that  the  walls  are  built  straight;  if  between  stud 
partitions  there  is  not  so  much  risk;  if  the  walls  are  crooked  and 
long  wide  flights,  the  best  way  is  to  put  them  together  in  the  build- 
ing. 

When  proceeding  to  cut  out  the  steps  and  risers,  consider  the 
thickness  of  lath  and  plaster,  the  base  and  depth  of  housings;  as 
the  walls  in  this  case  are  stud  partitions,  f  allow  X^^  on  each  side 
for  lath  and  plaster;  also  allow  the  strings  to  project  one  inch  [l^^J 
on  each  side  beyond  the  plaster  for  the  thickness  of  base;  allow 
three-quarters  of  an  inch  [H^^]   on  each  side  for  the  housings. 

Now  take  a  strip  a  little  longer  than  the  width  of  well,  setoff 
from  left  to  right  the  width  of  opening  [3^.  0^^],  then 
measure  to  the  left  for  the  plastering  and  base,  [Ji^''~'r]4^^-{- 
2'^=r:-3%'^J  equals  SH'^'  Now  ?/.  C  minus  3%^^  equals  2' 
8H^^  to  which  add  the  two  housings  [M'^-rM'^4-3^  8}4^^= 
V.  W4."\  equals  1'.  9%'^  for  the  total  length  of  steps  and 
risers;  they  should  be  cut  half  an  inch  longer  to  allow  for  squar- 
ing the  ends. 

*A  very  good  method  to  house  out  the  nosings  and  scotias,  is  to 
take  a  step,  shoulder  the  nosing  \"  from  the  end  down  to  the 
face  of  rise,  then  stand  the  step  in  the  housing  tliat  is  already  made 
in  the  string;  tlieu  with  a  fine  scribe  awl  mark  around  the  nosing 
earelully,  then  house  out  and  the  nosing  will  be  sure  to  come  up  close. 
The  same  method  is  applied  when  the  steps,  risers  and  scotias  are  all 
glued  up. 

tFor  brick  walls  %"  is  allowed  for  plaster,  and  for  stud  partitions 
li"  is  allowed  for  lath  and  plaster. 


1)2  Pirate  19. 

The  width  of  steps  equals  the  tread  [9'''']  plu9  the  projecting 
nosing*  [lU^^]  plus  the  tongue  [94^^]  into  the  rise  at  the  internal 
angle  D,  of  step  and  rise;  thus  Q''-\'iyi^'-^%^'=lQ%''  equals 
10>8  ^^  for  the  total  width  of  step.  The  width  to  get  out  the  risers 
equals  the  height  of  rise  [iH^  I  unless  the  risers  betongued  into 
the  steps,  then  allow  the  tongue  [h^^]  niore;  the  steps  should  be 
ploughed  }4^^  deep  to  receive  the  scotia  unless  in  very  common 
work. 

Now  square  and  cut  the  treads  and  risers  to  the  exact  length 
2^,  9M^':  take  two  trestles,  set  them  out  of  wind  and  place  tlie 
strinjis  on  edge  with  the  nosings  down,  enter  a  step  at  each  end, 
and  at  the  center,  wedge  them  slightlj'  and  tack  a  nail  in  each  end 
of  step,  then  square  the  flight  with  a  rod;  brace  and  nail  the  steps 
linn;  enter  the  balance  of  steps  and  risers,  glue,  wedge,  and  nail 
them  firm;  the  landing  step  leave  out  until  set  in  place  at  tlie 
building.  If  it  be  preferred  to  build  them  up  in  the  building, 
place  the  two  strings  in  place,  and  if  brick  walls,  mark  and  plug 
the  walls  every  tenth  course  in  the  horizontal  beds,  then  cut  and 
enter  the  first  rise,  and  also  the  two  upper  steps.  See  that  the 
strings  are  square  to  each  other  then  fix  in  place.  Now  cut  and 
fix  the  steps  and  risers  by  wedges  and  glue;  also  nailing  the  steps 
and  risers  from  above  and  also  below  for  good  stairs;  also  glue 
and  nail  blocks  00  firmly  in  the  angle;  cTZiC  shows  a  scantling 
underneath  to  which  rough  brackets  may  l>e  nailed  in  case  the 
steps  are  long. 

Fig.  4.  Shoivs  the  plan  of  a  close  stairs  havinfj  13  1'iscrs 
landing  on  a  quarter  pace,  with  one  rise  off  on  ejich  side,  this  rise 
off  the  quarter  pace,  should  be  avoided  if  possible  in  all  cases  as 
it  may  cause  stumbling  at  the  head  of  stairs.  'I'lie  construction  is 
the  same  as  explained  for  Fig.  1. 

Fig.  5.  Slwics  the  plan  of  a  close  ulairs  havhig  16  risers 
landing  on  a  quarter  pace  level  with  the  floor  above;  also  having 
a  quarter  pace  at  the  starting  one  rise  from  the  floor,  tin;  rise  is 
allowed  to  project  to  receive  the  door. 

Fig.  6.  Exhibits  the  plan  of  a  box  stairs  havvnrj  1?>  risers 
with  one  winder  and  two  risers  on  each  side  of  the  triangular 
pace.  This  form  of  a  stair  case  would  be  bad  in  a  dwelling  house 
where  there  are  children,  and  should  be  avoided  if  possible.  The 
plan  is  introduced  here  to  show  how  the  difficulty  may  be  overcome 
in  a  hampered  place;  the  treads  are  8^'. 

Fig.  7.  Shows  the  plan  of  a  iloiible  cpiartcr  pace,  liox  stair 
case,  having  20  risers.  The  lauding  rise  is  kept  away  from  the 
door;  at  the  starting  the  first  rise  projects  out  to  receive  the  door. 
The  treads  are  T%^^;  in  this  case  where  the  tread  is  narrow  the 
nosing  of  the  step  may  be  increased  a  little  over  the  general  rule, 
but  not  over  a  half  inch;  some  would  prefer  to  divide  each  quarter 
pace  into  two  steps  and  take  one  rise  from  the  short  branch 
landing,  so  as  to  give  more  room  at  the  door,  and  also  take  one 
rise  from  the  middle  branch,  and  thereby  increase  the  treads  to 
8>4.  At  the  starting  the  first  rise  could  project  out  beyond  the 
door  far  enough  to  receive  the  finish,  this  would  improve  the 
stairs,  although  some  will  not  allow  winders  of  any  kind  in  a 
house. 

Fig.  8.  Shows  the  plan  of  a  dovble  quarter  pace  ivindlng 
box  stairs  cnniainlixg  IG  risers.    Part  of  the  first  step  to  gain  ''run*' 


*As  a  rule  the  nosing  is  allowed  to  project  past  the  rise  equal  to 
the  thickness  of  steps. 


Plate  30.  93 

is  allowed  to  stand  out  in  tlie  room,  tlie  step  is  made  long  enough 
to  receive  the  finish  around  the  door.  For  want  of  space  three 
winders  are  placed  at  each  quarter  pace  divided  off  equally  on  the 
<iuarter  circle.  This  kind  ot  a  stair  case  should  not  be  used  in  a 
tirst-class  dwelling  house;  in  small  houses,  and  where  cramped 
lor  space,  the  stair-builder  has  often  to  resort  to  winders  as  the 
last  remedy. 

Fig.  9.  Shoios  plan  of  an  open  flight  in  a  hall  havimj  a 
platfonn  or  '■'half  pace."'  There  are  i'l  risers  to  the  platform, 
and  6  off,  18  risers  in  all.  This  type  of  a  stair  case  is  classed 
with  the  "dog-leg"  style.  There  is  no  cylinder  used.  The  rail 
occupies  Ihecenterof  hall  on  the  different  flights  both  ascendingto 
and  returning  from  the  platform,  and  a  vertical  plane  through  the 
center  of  balusters  would  be  the  center  of  hall. 

To  gain  room  at  the  starting  the  center  of  newel  post  is  placed 
at  the  face  of  second  rise,  and  the  first  rise  and  step  is  rounded 
off,  and  is  termed  a  '■'■hull  nosed  stej),"  The  newel  at  the  plat- 
form and  risers  is  so  constructed  that  the  face  of  No.  12  rise,  land- 
ing, and  the  face  of  No.  13  rise,  starting  off  the  platform,  is  oppo- 
site, and  lines  with  the  center  of  newel.  Sometimes  these  stairs 
are  lined  up  with  narrow  flooring,  smoothed  and  beaded,  and  cut 
off  liaud-rail  high  and  caped.  Sometimes  they  are  closed  in  with 
stud  partitions  and  plastered,  in  that  case  they  are  termed  close  or 
box  stairs.  Then  again  they  are  often  finished  witli  return  nos- 
ings and  brackets  on  an  outer  string,  having  rail,  balusters  and 
newels.  If  the  risers  be  niitered  to  the  string  and  no  brackets, 
the  strings  are  then  termed  '' qaaher  strings.^' 

Light.  Windows  should  be  so  placed  in  all  close  stairs  that 
sufficient  light  and  air  may  be  introduced,  so  those  passing  up  and 
down  may  not  stinnb'e:  also  that  the  dust  which  gathers  in  the 
corners  may  be  dusted  out  and  kept  clean;  and  for  ventilation, 
that  the  sun  and  air  may  enter,  sweeten  and  purify  the  atmospherf. 
within.  Dark  corners  in  all  cases  should  be  avoided;  "better 
not"  build  at  all,  than  build  a  house  with  disease  breeding  places 
in  it;  if  not  convenient  to  have  windows,  then  introduce  a  sky- 
light in  the  roof  if  possible. 


PLATE  20. 


Plate  20.  [Scale  fi^l  foot].  Exhibits  the  plan  of  a 
quarter  pace  having  t/iree  vnnders  for  a  box  stairs,  and  the 
manner  of  lining  olf  the  strings  and  ivindAng  steps;  the  rise 
is  7}.,"  bi/  Q^'  Iread.' 

Fig.  1.  Shows  the  plan  of  three  winders  in  a  quarter  pace 
connecting  the  flyers. 

The  opening  in  the  second  stoiy  is  framed  in  the  rough  3'. 
\}-4'^,  x,  X,  X,  shows  the  line  of  studs.  Make  xv7 equal  o'.  1)4" 
fur  the  width  of  opening  in  the  second  story;  at  J" is  shown  the 
thickness  of  the  wainscotiiii;- 1  f],  then  from  the  studs  to  center 
of  wainscoting  equals  Z'.  1". 

Make  1  2  and  I  3  each  equal  3'.  1";  at  ri^ht  angles  to  XX, 
draw  .3  0;  then  at  3  and  at  jiaht  angles  to  XX,  draw  2  O,  estab- 
lishing the  luiint  O;  at  O  >et  (.ff  the  newel  to  equal  b"yy\  the 
center  O  will  be  on  line  with  the  center  of  wainscoting.  A,  A, 
A,  A,  shows  the  face  <  f  wall  siring,  stt  out  from  siuds  IX^^;  for 
the  lath  and  plastering  \H^^]  and  for  the  thickness  of  base  [1^^]. 
Hi3" shows  the  string  [If.'"]  on  the  right. 


94  Plate  20. 

From  the  center  O  sweep  the  arc  BC  to  any  radius;  then 
divide  the  arc  into  three  equal  divisions  JBD,  DE  and  EC;  from 
the  center  O  draw  the  rise  OS  produced,  cutting  the  wall  string 
at  F.  Again  from  O,  draw  the  rise  OD  produced,  cutting  the 
wall  string  at  G.  Draw  the  straight  treads  4,  5,  6,  t^c,  parallel 
with  the  rise  O  3,  the  dotted  lines  show  the  projecting  nosing.  It 
will  be  noticed  that  if  the  face  side  of  No.  1  winder  be  turned  over 
it  will  answer  for  No.  3  winder,  but  the  grain  of  wood  will  run 
the  wrong  way. 

The  stair  builder  will  find  it  convenient  in  cutting  out  tlie 
winders  to  make  two  patterns  as  shown  at  Figs.  2  and  3.  They 
should  be  made  substantial  from  strips  and  braced,  that  they  may 
keep  their  shape  make  them  a  little  large  at  the  nosing;  also  allow 
for  the  tongue  on  the  back  edge;  they  should  be  longer  than  shown 
on  plan  so  they  may  be  made  to  answer  for  longer  steps.  For 
shorter  steps  an  additional  strip  tacked  on  at  the  wide  end  will  save 
an  extra  pattern. 

For  four  winders  in  a  quarter  pace  two  other  patterns  made 
in  the  same  way  will  be  found  to  save  time.  String  them  up  for 
future  use. 

Laying  out  the  icall  struKjs  for  loiudcrs. 

Pig.  4.     Shoivs  the  irall  string  starling. 

The  rise  equals  't}4^^,  No.  1  winder  measures  20>2^^  at  the 
wall  string,  then  take  the  steel  Sfjuare  with  20K^' on  the  blade 
and  7)^''''  on  the  tongue,  and  apply  it  to  the  edge  AB of  string;  draw 
the  face  of  rise  CD  from  the  tongue.  Now  set  a  bevel  to  tiie  line 
CD  and  draw  No.  1  rise  and  winder.  Set  up  at  D  the  height  of  rise 
[73^^'J  and  draw  No.  3  steji,  then  transfer  the  distance  fnmi  No. 
3  rise  to  the  corner  [HM^^]  on  plan,  Fig.  1,  and  allow  ^^^^  more 
for  the  tongue  shown  in  the  corner;  make  the  easing  at  Fto  suit; 
glue  on  a  triangular  piece  at  JGTto  form  the  easing  connecting  the 
regular  base;  draw  the  curves  lo  please  the  eye  and  suit  the  height 
of  base  and  string  in  the  corner. 

Proceed  in  the  same  manner  to  lay  off  the  wall  string  at  Fig. 
5.  The  bevel  is  shown,  also  the;  divisions  are  laid  off  to  corre- 
spond with  the  divisions  on  the  plan;  the  joint  at  i?  connecting 
the  straight  string  is  4K''  ftom  tiie  face  of  No.  4  rise;  instead  of 
a  tongue  in  the  corner  there  will  be  a  groove,  and  the  string  cut 
off  1  >8  ^''  from  tlie  face  edge  of  groove. 

Make  the  height  of  easing  in  the  corner  to  agree  with  that  at 
Fig.  4.  in  this  case  8'^  At  i?  a  portion  of  the  straight  string  is 
drawn  to  give  the  direction  of  the  straiglit  wall  string;  now  with 
a  flexible  strip,  draw  the  curve  tangent  to  the  straight  string  to 
suit  the  eye;  it  will  be  noticed  that  the  distance  from  the  external 
angle  of  No.  3  rise  to  the  curve  is  less  than  the  regular  distanc(! 
[4^'!,  while  at  No.  4  rise  the  distance  is  greater;  this  will  often 
happen  and  must  not  be  considered  a  serious  fault;  of  course,  it 
should  be  the  aim  to  have  the  margin  regular,  but  a  graceful 
curve  must  be  considered,  for  that  will  be  the  first  to  catch  the  eye. 

The  splice  at  R  is  made  with  a  tongue  and  groove;  this  is 
very  nicely  done  on  the  shaper  and  afterwards  fit  up  and  glued: 
when  dried  and  smoothed  off,  tack  or  screw  a  piece  of  board  2' 
long  on  temporarily  to  keep  the  joint  firm  while  hauling  to  the 
building;  this  can  be  made  a  neat  and  substantial  joint;  the  newel 
l>ost  is  ploughed  to  receive  the  wainscoting. 

Pig.  6.  Shoivs  the  manner  of  boring  and  cutting  in  the 
housings. 

AB  shows  the  gauge  line  run  on  from  the  face  of  string  far 
enough  down  to  allow  3X'^  to  4^'  from  the  external  angle  of  step 


Plate  ai.  95 

and  rise  to  the  edge  of  string;  at  Cfour  or  five  holes  are  bored 
';{"  deep;  and  at  D  they  are  shown  mortised  out  ready  to  apply 
tlie  back  saw  as  explained  for  Fig,  3,  Plate  19. 

Fig.  7.  Shows  Iww  to  find  the  stretch  of  pitchboard  for 
setting  the  compasses. 

Kun  a  light  gauge  line  AB  on  a  flat  surface,  turn  the  liypoth- 
euuse  of  pitchboard  down  on  the  gauge  line,  and  with  a  thin 
pointed  knife  blade  held  along  the  slope  of  rise  and  tread,  mark 
lightly  on  the  gauge  line  the  points  1  and  2;  then  set  the  com- 
passes carefully  to  the  distance  1  2,  for  the  stretch  of  pitchboard. 

Fig.  8.    Shows  Vie  housing  pattern. 

In  a  hand  shop  this  pattern  will  be  found  very  handy  when 
laying  off  the  housings  for  the  tread,  rit-e  and  wedge  room. 

Fig.  9.  Shows  a  templet  for  savnng  ou^  the  wedges  with 
Vie  circular  saw. 

Where  the  stair-builder  is  favored  with  steam  power,  very 
little  material  in  a  stair  shop  need  be  wasted.  A  shows  the  saw 
guide;  JE3  a  piece  of  board  about  2',  0'^  long,  and  5  wide;  the 
thickness  is  [!"]  shown  in  elevation  at  C,  having  a  handle  D, 
and  ]iotehf  d  out  at  JE,  tiie  size  of  wedge,  the  saw  is  shown  at  F. 

In  a  stair  shop  very  littleslcK'k  need  kg  to  waste;  all  the  cuttings 
may  be  collected  und  plied  away  until  a  slack  tiuio  comes,  then 
sawed  up  into  wedges  and  triangular  blocks  to  glue  in  the  internal 
angle  of  step  and  rise;  also  into  circular  nosings,  scotias  and  easing 
on  wall,  and  front  strings,  and  many  other  little  things  for  the  turn- 
ing lathe.  Mind  economy  is  the  secret  of  success  in  all  branches  of 
liusiness. 


PLATE  21. 

Plate  21.  Exhibits  the  construction  of  palter  as  for  a  waU 
rail  on  unnders  for  a  box  stairs;  the  plan  of  risers  and  treads 
corresponds  to  Fig.  1,  Plate  20.  Therailis  2y/'  wide  by  :i):i^' 
deep.* 

Figs.  1  and  2.  [Scale  ?i'"=^l  foot].  Shows  the  plan  and 
elevation;  1,  2,  3,  indicate  the  position  of  risers  for  the  three  wind- 
ing treads  on  plan;  4.  5,  6,  show  the  risers  for  tlie  straight  treads. 
A,  A,  A,  shows  the  lino  of  i)laster  from  which  the  center  of  rail 
is  set  out  3}.<^^.  The  wall  rail  is  2X '''  wide,  thus  allowing  a  space 
for  the  hand  between  the  wall  and  rail  of  2}^^^^.  This  is  optional 
with  the  stair-builder,  the  space,  however,  should  not  be  less  than 
Ij-y^  between  the  wall  and  rail. 

The  rail  is  shown  starting  out  of  a  rosette  at  JHTand  couliuu- 
ing  up  and  terminating  in  the  architrave  or  finish  around  door  at 
the  landing.  At  XXX  are  shown  iron  ' '  hold-fasts,"  or  brackets. 
To  support  the  rail  they  should  screw  into  the  studs  or  into  pieces 
cut  between  the  studs  as  shown  at  S;  this  should  be  altcMided  to 
before  the  lathing  is  done;  if  brick  walls,  then  blocks  should  be 
placed  in  the  walls  every  4^.  C  for  the  hoid-fasts. 

Now  lay  off  the  center  line  of  rail  DDD  on  plan  3>./'  from 
the  line  of  plaster,  make  quarter  turn  in  the  corner  to  whatever 
radius  desired,  say  6",  then  make  DE  and  D^each  euual  ()"  and 
at  right  angles  to  jD J' and  .£72?,  draw  J70  and  J'O,  establishing 
jthe  parallelogram  EDFO;  then  with  O  as  a  center  and  OE  for  a 

*In  specifying  timber  the  horizontal  measure  is  first  mentioned, 
and  the  vertical  measure  last;  as  for  a  joist  3"X10"  means  that  the 
10"  way  is  vertical  and  the  2"  is  horizoutal, 


UC  Platk  31. 

tadius  draw  the  curve  for  the  center  line  of  rail  from  E  to  F. 
Join  FE  for  the  chord.  Now  marli  the  treads  on  the  center  line 
of  rail;  from  the  joint  at  D  to  face  of  No.  I  rise  is  \i''\  from  No. 
1  rise  to  No.  2  equals  18^^^.  From  No.  2  rise  to  E,  the  spring  of 
quarter  turn,  1)4^'.  Then  from  F  to  No.  3  rise  7K,  and  from  No. 
3  rise  to  No.  4  rise  18X,  and  from  No.  4  rise  to  No.  5  rise  9". 
For  the  inclination  of  the  straight  rail  the  common  pitch  is  7,'i'' 
rise  by  9'^  tread. 

Fig.  2.  Shows  the  deration  and  development  of  the  treads, 
risers  and  tangents  corresponding  to  the  center  line  of  rail  on 
plan. 

First  take  the  average  pitch  of  5  risers  around  the  winders  on 
the  center  line  of  rail,  thus:  From  D  to  face  of  No.  I  rise  on 
plan,  equals  12^^  to  No.  2  rise  18>^'',  to  No.  3  rise  around  the 
angle  of  tangents  equals  27'',  to  No.  4  rise  equals  18 ^.j",  and  one 
straight  tread  9",  makes  a  total  (12"4-183?/'4-27"-l-18K"+9" 
=85")  equal  to  85",  which  being  divided  by  the  number  of  lisers 
(.5-f-85^'=17")  equals  17"  for  the  average  tread. 

Now  let  XX  indicate  the  edge  of  drawing  board,  then  with 
the  steel  square  take  17"  on  the  blade  and  the  height  of  rise 
(73^")  on  the  tongue,  apply  to  the  edge  of  board  and  draw  the 
perpendiculars  EG,  DN  and  FJ  from  the  tongue  to  agree 
with  tangents  ED  and  DF,  on  plan,  Fig,  1.  Elevate  the 
treads  and  risers,  keeping  the  face  of  No.  3  and  3  rise  7'^"  from 
the  spring  lines  as  shown,  corresponding  to  plan,  Fig.  1.  At  the 
external  angle  of  the  treads  and  risers  set  off  the  half  depth 
[!%"]  of  rail  as  shown  by  the  arcs,  then  draw  lines  AB  and 
CK"  indefinite,  to  tangent  the  arcs  for  the  center  of  rail. 

At  Qset  up  4''' to  underside  of  rail  and  l?.i"more  to  Z»  the  cen- 
ter of  rail.  Dx&w  LA  parallel  to  the  floor  line,  cutting  AB  at  A. 
Prolong  No.  2  rise  to  cut  AB  at  B,  also  prolong  No.  3  ris'i.  Make 
3  ilf  equal  2  B,  join  BM  jnoduced,  rutting  CK  at  C.  also  cutting 
the  perpendiculars  EG,  DH  and  JVat  6,  7  and  8;  then  6  7  and 
7  8  show  the  increased  length  of  tangents  in  elevation. 

Now  ease  off  the  angles  at  A,  B  and  C  to  please  the  eye. 
using  a  flexible  strip,  being  careful  to  draw  the  curves  tangent  to 
the  center  lines  at  the  joints.  Next  set  off  the  half  depth  of  rail 
[1%"]  on  each  side  of  center  line  for  the  ramp  patterns.  The 
pattern  for  the  level  quarter  turn  at  L  is  shown  at  JEf  on  plan. 
At  right  angles  to  EG  draw  6  N,  cutting  DH  ^t  R,  then  iVS  is 
the  height  the  wreath-piece  will  rise  from  E  io  F  on  plan. 

Make  iVJP  equal  the  cliord  EF,  Fig.  1 ;  from  JR  and  at  right 
angles  to  6  8,  draw  BS.  Taraliel  with  DH  draw  the  half  width 
of  rail,  cutting  the  tangent  6  7  at  10  for  the  increased  width  of 
face-mould  on  the  radial  lines. 

Fig.  3.     Shines  the  facc-monld. 

The  tangents6  7  and  7  8  in  elevation  are  the  same  length,  hence 
there  will  be  but  one  bevel  required.  Select  a  piece  of  heavy 
paper,  draw  the  right  line  7  8  produced  to  t:  make  7  8  t  equal 
7  8  Tin  elevation;  then  with  8  P  in  elevation  as  a  radius,  and  8 
for  a  center,  draw  are  at  6,  then  with  8  7  as  a  radius  and  7  for  a 
center,  draw  arc  intersecting  at  6;  also  with  the  same  radius  and 
the  points  6  and  8  as  centeis  draw  arcs  intersecting  at  0;  join  6 
7,  6  0  and  O  8,  and  we  have  the  parallelogram  0  8  7  6. 

Proof.  If  the  diagonal  0  7  equals  the  diagonal  OD  on  plan. 
Fig,  1,  the  parallelogram  is  correct. 

On  the  radial  lines  6  O  and  8  0,  make  6  1,6  2  and  S  1.  8  2,  each 
equal  7  10  in  elevation.  On  the  diagonal  0  7,  make  0  3  equal  the 
radius  O  3  on  plan.  On  each  side  of  3  set  off  the  half  width  of 
rail  {IVi).  _  ,  .         . 


Plate  31  ,«7 

Now  pivot  the  trammel  iu  0  and  set  the  arms  at  right  angles 
to  the  diagoual  O  7,  for  in  tliis  case  the  diagonal  is  the  direction  of 
the  minor- axis.  Set  from  pencil  to  minor- piu  the  distance  O  3  for 
the  center  line,  leaving  the  uiajor-pin  loose.  Then  plaoe  the  pen- 
cil iu  8,  drop  the  pins  iu  the  grooves,  hold  the  trammel  firai.  Now 
fasten  the  niajor-piu  and  draw  the  center  line  6,  3,  8.  Next  draw 
the  convex  curve,  set  from  pencil  to  minor-piu  the  distance  O  4. 
(the  trammel  remaining  as  before)  place  the  pencil  in  2  and  drop 
the  pins  in  the  grooves,  then  fasten  the  major-pin  and  trace  the 
curve  3,  4,  2,  for  the  outside  of  mould.  For  the  inside  or  concave 
side  set  from  pencil  to  minor-pin  the  distance  5  0.  Now  place  tlie 
pencil  in  1  and  drop  the  pins  in  the  grooves,  then  fasten  themajor- 
piu  aud  trace  the  concave  side  1,  5,  1,  of  mould. 

Make  the  joint  at  6  perpeudicular  to  tangent  7  6;  from  1  aud 
2  draw  the  width  of  shank  parallel  to  tangent  7  t:  at  t  make 
joint  at  right  angles  to  tangent  1 7. 

Bevel.  Make  OS  on  plan  equal  RS  in  elevation;  join  SE, 
then  in  the  angle  OSE  is  found  the  bevel  for  both  joints;  they 
will  cross  the  tangents. 

The  application  of  bevels  are  shown  at  sections  a  and  b;  the 
dotted  line  shows  the  gauge  line  and  tlie  tangent  line  squared 
across  the  joint,  gives  the  center  through  which  to  apply  the 
bevel;  the  block  pattern  is  applied  square  to  the  bevel,  and  gives 
the  twit^t  of  rail  at  the  joints;  the  shaded  parts  show  the  amount 
of  ov'r  wood  that  has  to  come  off.  The  sliding  of  the  mould  is 
shown  at  I'late  24. 

If  a  round  rail  is  required,  as  shown  at  Fig.  4,  then  draw  the 
l)ara!lelogram  0  S  7  (5,  and  draw  the  center  line  of  rail  8  3  6,  with 
the  trammel,  make  joints  at  t  and  6  as  at  Fig.  3,  Then  set  off 
the  half  width  of  rail  [U4 ''j  on  each  sid«  of  the  center  line  as 
shown.  For  a  round  rail  the  thickness  of  plank  required,  need 
be  only  a  slight  increase  over  the  diameter  of  rail,  just  enough  to 
dress,  because  the  elliptic  curve,  passing  through  the  center  of 
wreath-piece,  gives  the  correct  "falling  line,"  and  as  the  center 
of  a  round  rail  is  eiiui-distant  from  the  circumference  in  all  its 
parts,  the  wreath  when  iu  position,  must  be  correct. 

At  sections  a  and  b,  the  shaded  part  shows  the  amount  of 
over  wood  that  lias  to  come  oft";  if  the  bevel  be  applieil  through 
the  center,  as  at  Fig.  3,  it  will  give  the  direction  to  bore  for  the 
bolt  nuts. 

Fig.  5.     Shows  the  wreath-piece  landing. 

This  face-mould  is  the  most  simple  to  draw  in  stair  building, 
as  the  plank  is  not  sprung;  the  lines  can  all  be  taken  from  the 
pitchboard,  (except  the  trace  of  mould),  including  the  bevel  shown 
at  8. 

First  draw  the  parallelogram  OAbD  for  the  center  of  rail  on 
plan;  elevate  rise  No.  16  perpendicular  to  cb,  and  at  any  point, 
draw  the  pitchboard  e/g*  at  right  angles  to  No.  16  rise;  prolong 
the  hypothenuse  eg*  indefinite.  From  points  c.  A,  3,  D,  and  4, 
on  plan,  draw  lines  parallel  with  No.  1(3  rise,  culling  the  pitch 
line  eH  at  5,  6.  7,  8  and  H.  Then  again,  draw  lines  indefinite 
from  the  same  points  perpendicular  to  the  inclination  eH. 

Face-mould.  Now  parallel  with  the  inclination  draw  cab 
in  elevation,  make  ao  and  bd  equal  AO  and  bD  on  plan;  join 
od  and  prolonged,  establishing  the  parallelogram  oabd  on  the 
cutting  plaiie;  the  points  3  and  h  show  the  increased  width  of 
mould  at  joint;  add  on  straight  wood  parallel  with  3  h  sufficient 
to  let  iu  and  fasten  to  the  architrave. 


98  Plate  21 

The  line  od  is  the  semi-major  axis,  and  the  line  oa  is  the 
Bemi-minor  axis,  the  trammel  centers  in  0;  make  aj  and  ak  each 
equal  the  half  width  of  rail;  now  trace  the  curve  for  the  inside 
and  outside  of  mould,  as  has  been  explained.  From  j  and  k  draw 
lines  parallel  with  the  tangents  cb  for  the  shank,  the  joint  at  c  is 
at  right  angles  to  the  tangent  cb,  and  is  drawn  to  agree  with 
joint  c.  on  plan. 

The  section  at  b  shows  the  bevel  applied  in  the  usual  way; 
at  joint  A  the  square  is  shown  applied  from  the  face  of  plauk 
because  there  is  no  spring  in  this  case;  the  shaded  part  shows  the 
required  thickness  and  breadth  of  plank  to  contain  the  twist  of 
wreath-piece.  In  this  case  the  pitehboard  gives  the  correct 
Bevel. 

Fig.  6.    Slioivs  a  section  of  round  rail  H  full  size. 

The  dark  shade  sliows  the  iron  bolt,  the  light  shading  shows 
the  hollow  dowel  through  which  the  rail  bolt  is  to  pass  freely; 
this  hollow  dowel  answers  a  good  purpose;  J^  '^  is  a  good  size, 
they  enter  the  rail  about  y^''  on  each  side  of  the  joint,  and  are 
glued  in  on  one  side  at  the  bench.  Then  bore  through  the  dowel 
for  the  bolt.  For  round  rails  and  center  joints  of  moulded  rails, 
they  suit  well. 

Figs.  7  and  8.  Exhibits  a  handled  scraper  one-half  full 
size. 

This  is  found  a  good  tool  for  moulding  the  twist  part  of  a 
hand  rail;  they  may  be  made  of  all  sizes  and  patterns,  the  draw- 
ing explains  itself.  Fig,  7  shows  the  length  of  scraper.  Fig.  8 
shows  a  cross  section  of  the  same;  iifJ^T shows  the  handles,  JB, 
the  steel  bit;  C,  the  cap  held  down  by  the  set  screws  iSfif  In  cross 
section;  T  shows  the  throat;  apple  tree  is  a  very  good  wood  from 
which  to  make  this  tool;  the  cap  at  C  may  be  made  from  some 
harder  wood. 

Figs.  9,  10  and  11.  Sliows  a  dovetail  patt<:ni,  (Scale 
X  full  size). 

Every  stairbuilder  has  his  own  way  of  la>  ing  olf  dovetails. 
This  pattern  is  introduced  here  as  a  handy  means  to  lay  oil"  the 
work  in  a  hand  shop  where  something  of  the  kind  is  needed.  Mr. 
Parry  has  a  dovetailer  he  furnishes  with  his  router  that  saves  all 
the  trouble  of  laying  off  the  dovetails. 

Fig.  9.     Shows  the  front  of  tool. 

Fig.  10,  the  side  and  Fig.  11,  a  cross  section.  A  is  the 
stem  2}i''yji^^  thick,  and  is  Including  the  guard  B  1"^'  long. 
A  slot  %''y,W  is  shown  at  C  rebated  on  one  side  as  shown  at 
J,  Fig.  11,  the  guard  is  11^''  long  and  %"yiH"  in  cross  section, 
having  a  projecting  lip  D,  Fig.  10.  E,  E,  E,  E,  shows  tlie  size 
of  mortise  on  top  of  the  step.  F,  F,  F,  shows  the  size  of  dove- 
tails and  are  made  fast  to  the  pieces  EE,  as  shown  at  H,  Fig.  li. 
i  is  the  binder.  MM  are  set  screws,  having  washers  JVJV'and 
nut  in  the  binder  to  adjust  the  pattern  for  the  different  widths  of 
steps.  The  binder  keeps  the  dovetail  pattern  square  on  the  stem. 
'  This  pattern  is  intended  to  apply  on  the  stops  before  tlie  ends 
of  steps  are  cut  off  for  the  return  nosings.*  Some  stair-build- 
ers prefer  this  method.  It  will  be  observed  the  pattern  is  revers- 
able  for  either  right  or  left  hand  stairs,  and  should  be  nuide  of 
cherry  or  some  hard  wood. 

*The  ends  of  steps  are  cut  olT  when  the  nosings  and  brackets  are 
to  bo  tit  on  iu  tlio  building  wbeu  putting  up  the  rail. 


Plate  22  99 

Figs.  12  and  13.  Exhibits  the  face  and  end  view  of  the 
"  Cupper  gauge"*    [Scale  U  full  size]. 

A  is  the  stock,  B  is  tlie  stem  adjusted  by  the  set  screw  D, 
and  holdiug  a  long  tooth  C  made  of  steel,  and  held  in  place  by  a 
key  E. 

Pig.  13.  Sliows  an  end  view  of  the  same. 
The  stair-builder  should  have  different  sizes  of  this  tool,  some 
holding  a  pencil  and  others  steel  points.  They  are  very  handy  In 
squaring  the  wreath  part  of  rail.  After  workinar  tlie  concave  side  of 
wreath-piece  to  the  plurab,  the  convex  or  outside  may  be  easily 
;iauged;  also  Tchen  moulding  the  wreath  part  of  rail  the  gauge  will  be 
found  handy  in  tracing  the  different  members  around  the  twist,  espe- 
cially in  double  rails. 


PLATE  22. 


Plate  22.  Exhibits  the  plan  and  elevation  of  a.  platform 
or  half -pace  stair  case;  and  also  Jww  to  construct  the  cyliyider 
and  strings  for  the  same. 

Figs.  1  and  2.  Shows  the  plan  and  elevation.  [Scale, 
^//=1  loot]. 

f  The  height  of  story  is  10^  6'^;  the  width  of  hall  equals  6', 
3'^;  width  of  joist  in  the  second  story  equals  10^^;  the  door  under 
the  platform  is  6^,  S^''  high;  the  run  from  the  face  of  No.  1  rise, 
including  the  platfonn  and  cylinder,  is  14^.  2'^;  the  steps  are  to 
be  1>4^'  thick,  and  returned  ou  the  outer  string.  The  rail  is  3%'" 
wide  by  2}i^^  deep;  balusters  are  2'''X-''^;  the  newel  post, 
^z/y^//.  tjie  cylinder  7'^  diameter;  the  rail  is  on  the  right 
ascending,  therefore  is  termed  a  ''right  hand  rail"  There  are  to 
be  18  risers,  and  the  height  is  10^  G'^  then  10^  6^'  reduced  to 
inches  (10^  6''^X12^^— 12'j''^)  equals  126''',  which  being  divided  by 
the  number  of  risers,  IS.  (126''-^18=7'')  equals  7'''  for  each  rise, 
as  shown  on  story  rod  XX  in  elevation,  Fig.  3. 

The  height  of  door  under  the  platform  is  6^  8",  and  we 
should  have  at  least  C/^  over  the  door  for  the  casing  or  finish;  the 
platform  joist  is  10^''  deep;  the  lath  and  plaster  is  X'''  and  the 
floor  on  the  platform  is  %^^  thick.  Then  the  whole  height  from 
floor  (6^,  8'M-6'''-r>8''-r;-s'^n-lO''^97M")  equals  97%'^;  now 
14  risers  at  7^''  each  equals  98'^  making  8',  3'^  from  floor  to  top 
of  platform,  thus  allowing  the  space  required  under  the  platform 
lor  door  ami  finish. 

For  the  relative  width  of  tread  to  the  height  of  rise  for  dwel 
lings  if  practicable,  use  Bloudel's  constant  of  24  inches,   from 

which  take  twice  the  rise  (24^'— i^'— 7''r=l0'0  equals  ICfor  t  e 
width  of  each  tread. 

Now  we  have  for  the  run  of  stairs  including  the  platform  an 
cylinder,  14',  2'';  there  is  always  one  full  step  less  than  there  ar? 
risers  in  the  run  of  a  flight  of  stairs,  and  as  we  have  a  run  of  14 
risers  to  the  platform,  there  will  be  i;j  full  treads  and  one  landing. 

♦Termed  this  because  5Ir.  Cupper  was  the  first  to  introduce  the 
tool  in  print  for  the  stairbuilder 

tW'hcn  takinpr  the  height  of  story  the  stair-builder  will  do  well  to 
try  his  lod  at  ditlerent  points,  as  sometimes  the  joist  are  out  of  level 
and  mia,ht  cause  troul:)le;  therefoi'e,  care  in  this  particular  shouid 
not  bo  neglected;  the  best  point  to  take  the  height  is  at  the  starting 
of  the  first  rise.  Also  let  tlie  young  man  think  twice  before  setting 
down  one  Item  in  his  dimension  book,  for  a  mistake  of  a  few  inches 
may  cause  the  whole  flight  to  be  got  out  the  second  time. 


100  Plate  22. 

Then  13  treads  at  10'''  each,  equals  130'',  or  10^  IC  for  the 
run,  and  4'^  more  for  tlie  cylinder,  equals  11'',  2'^;  then  14^  2'''' 
minus  11',  1"  leaves  S',  0''  lor  to  frame  the  platform  iu  the 
rough,  as  shown  at  Fig.  1;  the  width  of  platform  should  equal 
the  half  width  of  hall,  more  is  better  and  less  crowds  the  passage 
between  the  rail  and  wall. 

The  next  will  be  the  flight  off  the  platform,  there  are  4  ri.sers 
and  three  full  treads,  at  W  each,  equals  2',  (}'',  and  one  lauding, 
for  which  allow  6''  for  the  rough  bearer  to  catch  well  on  to  thv 
joist  at  the  lauding;  also  allow  3'.  0'',  for  tlie  platform,  and  4" 
for  the  cylinder,  (2',  6''H-6''  ;-3',  C-t-4=6',  4'').  thus  making 
the  whole  distance  from  the  wall  to  the  joist  at  the  landing  0',  \" 
to  allow  for  the  flight  off  the  platl'orni. 

The  next  is  to  determine  the  "  headway;"  that  should  be  T'. 
C'  at  least,  more  i-s  better,  but  in  cramped  places  the  .stair-builder 
has  often  to  do  with  less.  AVhen  the  lu-adway  is  cut  short  it 
destroys  the  good  effect  that  the  stairs  wouid  otherwij;e  have  if 
there  was  more  headroom.  A  good  allowance  is  8'.  C,  when- 
e\er  it  is  convenient  to  have  it. 

Now  we  will  count  down  14  ri.sers  from  the  landing  at  7" 
each,  minus  the  joist  {W),  plastering  (1''),  flooring  {\"),  (14X7" 
=98''— iO'''+l''-fr'"=8G''--12''=;7'.2'0  equals  7'.  2"  for  the 
headroom.  Xow  place  the  face  of  headway  joist  plumb  over  Xo.  15 
rise,  numbering  down  from  above  as  .shown  in  elevation;  or  the  hori- 
zontal distance  from  the  wall  to  the  headway  joist  will  equal  3'. 
0"  for  the  platform,  4"  for  cylinder,  and  10  tj^'eadsat  10"  each,  and 
l"for  fascia  {?>'.  0''+4''+l6xiO'^^l^''''^8'-4''+l'':^;]l'.  9'') 
eciuais  11'.  U",  as  .shown  on  plan. 

The  next  is  to  decide  the  width  of  landing  in  the  second  floor. 
The  width  of  hall  is  G'.  2"  in  the  rough,  ami  we  have  to  provide 
for  a  7"  cylinder,  and  the  center  of  cylinder  will  be  the  center  of 
hall.  The  face  string  is  oiie  (I")  inch  thick.  The  center  of  hall 
IS  3'.  1"  from  wall.  (;3'.  l"i;]j.^"-l"^^^3'.  .'>'.'").  Hence  the 
\s  idth  of  well  equals  3'.  .5} ,'".  and  the  width  of  framing  will  equal 
('/.  S"  minus  3'.  hM",  or  2'.  83^"  for  the  width  of  framing  at  the 
landins.  The  length  will  Ijc  11'.  9"  minus  6'.  4",  the  space  for 
the  flight  oif  the  platform;  equals  {11'.  9"— 6'.  4":=  5'.  5"),  for 
the  length  of  trimming  :^' .  5"  by  2'.  8K"  in  width  as  shown  on 
plan,  Fig.  1. 

Fig.  3.  (.Scale  1)4" ^^\  foot).  Sluncs  how  to  place  the 
risers  in  the  cyUiider  so  o-s  to  qivc  the  same  inclination  .to  the 
wreath  of  cylinfJcr  tluit  the  fftraUjht,  part  of  slrimj  has. 

Draw  AJB  indefinite  and  parallel  to  the  edge  of  drawing  board 
ICX,  set  the  compasses  to  :>',;",  and  with  O  as  a  center,  draw  the 
semi-circle  ACB,  draw  OC  at  riglit  angles  to  AJ3,  also  from  A 
andS  draw  the  clirection  of  the  straight  part  f)f  outc.-r  string  per- 
pendicular to  XX;  With  A  for  a  center  and  AB  as  a  radius,  draw 
arc  at  Y;  again  with  the  same  radius  and  B  as  a  center  draw  the 
intersection  at  Y",  draw  KL  parallel  to  XX  and  to  tangent  the 
point  C.  From  Y  amA  through  A  and  J5  draw  lines  to  intersect 
KL  at  the  poi^its  K  and  L;  then  KL  is  the  stretchout  of  the 
semi-circle  ACB.     The  treads  are  10",  make  CM" and  CiVeach 

The  stair-buiir'c;"  should  mnke  tiie  above  calculation  in  the  build- 
ing when  takinii  tie  dm.pn-ions  lor  tli--  stan-s.  He  wiil  save  time  by 
calling  the  atiOEt'on  tf  the  f  reman  oarpentev  to  llio  .startinss  and 
liiidin^s,  raavkir.K  ■^■hf'vp  the  jjist  must  be  trimmed  to  and  floors  laid 
for  all  straight  stairs.  Thl.<5  can  easily  le  done  in  the  buildnig.  For 
winders  the  be.st  way  is  to  make  a  plan  to  a  scale.  And  all  trininiinjr 
laid  off  fi-om  the  dia^svin?.  All  measurcaionts  should  ba  cai-efuily 
noted  In  the  book  for  dimensiona. 


Flatk  23.  101 

e(iual  to  half  a  tiea<l  (5''^+5^'=10^0.  draw  YM  and  YN,  cutting 
the  line  of  cylinder  at  -.1  ami  3.  Draw  the  face  of  risers  3  J*  and 
■>D  i)arallel  witli  AB,  and  we  have  the  position  of  risers  in  the 
ry  Under. 

The  manner  of  placing  risers  in  the  cylinder  is  explainetl  at 
Plate  15. 

Fig.  4.    Shows  the  same  plan  as  at  Fig.  3  on  the  string  line. 

NN  shows  the  nosing,  C  the  string.  The  risers  are  .shoul- 
dered to  receive  the  thickness  (1^^)  of  string,  and  a  U'^  is  allowed 
to  ]>roject  and  miter  with  the  bracket,  the  nosings  project  over  the 
rise  equal  to  their  thickness  {l)i"),  and  are  shown  mitered  atthe 
ends  to  return  over  the  brackets.  The  treads  are  W\  hence  the 
balusters  will  be  spaced  half  a  tread  (5''^)  from  center  to  center  as 
shown  at  A  and  X.  Observe  the  two  face  sides  of  baluster  at  A 
line  with  the  face  of  rise,  and  also  with  the  face  of  bracket  line. 
The  mortise  for  dovetail  is  shown  in  the  center  of  baluster. 

Fig.  5.     Shows  how  to  lay  off  the  staves  foi'  a  1"  cylinder. 

AC  indicates  a  gauge  line  run  on  the  draft  board  a  conveni- 
ent distance  from  the  edge.  tSet  the  compasses  toa  radius  of  syi^^ 
and  with  O  as  a  center  draw  the  semi-circle  IBD.  With  the  same 
ra<tius  space  otf  the  semicircle  into  three  equal  parts  as  1  2  for 
one  sta\  e,  draw  O  2  prolonged  for  the  joint  of  stave,  and  join  1  2 
for  the  face  of  stave.     The  shaded  part  shows  its  thickness  {1}4^^). 

Th(;  angle  O  1  2  gives  the  bevel  for  the  staves,  or  as  shown. 
Ilie  angle  A  O  3  gives  the  bevel  in  this  case. 

The  shaded  ])art  at  D  shows  the  stave  for  the  quarter  cylinder 
and  the  bevel  for  the  same.  One  drawing,  that  at  Fig.  4  will  do 
lor  Fig.  3  and  Fig.  .5.  To  make  the  drawing  plain  and  not  con- 
fuse (he  learner,  it  is  thought  best  to  separate  them,  thatthe lines 
may  be  more  easily  understood. 

Fig.  7.  Shows  how  to  lay  out  the  front  string  and  connect 
the  same  with  the  cylinder. 

The  mode  of  finding  the  stretch  of  pitchboard  and  how  to  lay 
olT  the  wall  string  has  been  explained  for  Fig.  1,  Plate  19,  and 
also  Fig.  7,  Plate  20.  The  wall  string  should  be  laid  off  first,  and 
is  done  in  the  same  manner  as  above. 

Now  take  the  outer  string  run  a  light  gauge  line  BC  from 
the  lower  edge,  a  distance  equal  to  X^^  for  the  lath  and  plaster, 
and  4^'  for  the  rough  horse,  and  V^  more  for  the  rough  horse  or 
scantling  to  clear  the  back  of  rise  and  tread,  (]4^^-}-i^^-{-V^=5]4^^) 
equal  to  5%^^  from  the  lower  edge. 

It  is  supposed  the  lines  on  the  wall  string  have  been  laid  off 
and  the  internal  angles  of  step  and  rise  are  squared  over  to  the 
edge  of  string  as  shown  at  the  points  3,  3,  3,  Fig,  2,  Plate  19. 

Now  lay  the  wall  string  down  on  the  bench  with  the  face  side 
up,  take  the  outer  string  and  turn  the  face  side  down  on  the  wall 
string  with  the  lower  edge  to  the  upper  edge  of  wall  string;  then 
transfer  the  divisions  3,  3.  3,  &c.,  from  the  wall  string  to  the 
front  or  outer  string,  and  square  the  divisions  over  to  the  gauge 
line,  BC,  then  apply  the  pitchboard  along  the  gauge  line  as 
shown  at  A,  Fig,  7,  and  mark  around  the  external  angle  of  step 
and  rise  with  a  suitable  blade,  keeping  the  hypotbenuse  of  pitch- 
board  close  to  the  gauge  line  BC;  in  this  way  the  front  and  wall 
strings  will  agree  and  no  trouble  will  be  experienced  when  step- 
ping up  the  stairs;  the  reason  for  running  the  gauge  line  on  from 
lower  edge  of  front  string  is,  often  the  board  selected  for  the 
string  will  not  hold  the  full  width,  and  the  triangular  pieces  that 


102  Plate  22. 

cut  out  may  he  glued  on,  and  thus  increase  the  string  to 
the  required  width.  Malce  the  distance  from  Xo.  13  rise  to  joint 
of  cylinder  equal  to  the  corresponding  distance  AB,  (8X'^)  on 
plan  Fig.  7.  INIal^e  joint  25.27  perpendicular  to  No.  13  tread,  par- 
allel with  the  joint  DE  add  on  %'^  for  tongue.  At  F  glue  on  a 
triangular  piece  to  form  the  ea.sing.  The  easment  pattern  K  \>- 
shown  applied;  GH  shows  the  joint  of  cylinder  at  the  turn- 
out. The  fii"st  rise  is  sliown  reduced  the  thickness  of  a  step. 
(XH^^)  so  that  the  height  of  the  rise  will  be  the  same  as  the  regu- 
lar height  when  the  .step  is  in  place. 

Fig.  8.    Shoxvs  the  shott  front  string  off  the  platform. 

This  string  is  laid  off  from  the  wall  string  in  the  same  man- 
ner as  Fig.  7.  Make  the  distance  from  No.  10  rise  to  the  joint 
of  cylinder  AD  to  equal  9%^^  as  sliown  on  plan,  Fig.  4,  and  draw 
A2?  perpendicular  to  No.  15  tread.  Parallel  with  the  joint  AZ) 
add  on  %^^  for  the  tongue.  At  KE  is  shown  the  end  view  of 
same.  At  ilf  the  string  is  notched  }i^^,  because  the  steps  are  that 
much  thicker  than  the  flooring,  and  tliis  allows  the  string  at  that 
point  to  come  close  under  the  flooring.  For  the  width  of 
string  at  the  easing  allow  10^''  for  the  joist,  and  for  lath  andplastei- 
%^^  equals  lOK.  Now  make  MG  equal  lOX,  aud  draw  the  line  at 
G  parallel  with  the  floor  line  EM.  Then  u.se  the  easing  pattern  for 
the  curve  of  easment.  A  saw  kerf  is  shown  at  the  end  for  join- 
ing the  level  fascia  or  string. 

Fig.  9.  [Scale,  %^^=1  foot].  ExMbiis  the  elevation  of 
staves,  to  obtain  their  different  lenghts. 

This  drawing  may  be  made  on  the  back  of  cylinder  board,  and 
used  for  subsequent  like  cylinders;  apply  the  hypothenuse  of 
pitehboard  to  the  edge  of  draft  board,  and  along  the  tread  draw 
the  line  AB  indefinite.  Make  1  2,  2  3.  3  4,  eacli  equal  the  back 
of  stave  3  3,  Fig.  10;  perpendicular  to  AB  draw  1  8,  2  7,  3  6,  4  5, 
indefinite.  Make  1  8  equal  DE.  Fig.  7,  plus  the  height  of  a  rise 
[15'^];  also  make  4  5  equal  i?Z>,  Fig.  8.  \1"].  Draw  8  .5  for 
the  length  of  staves,  they  should  be  cut  longer  for  trimming,  as 
shown. 

For  ordinary  work  that  Is  painled,  this  raethotl  of  staving  up  a 
cylinder  can  be  made  a  good  job,  but  for  hard  wood  tiaish  with  large 
cylinders  they  should  be  built  di&'ereutiy :  that  is,  the  grain  of  wood, 
instead  of  beinjj  perpendicular  to  the  treads,  should  run  in  the  direc- 
tion of  the  straight  string  lor  all  fli'st-class  work;  this  requires  more 
labor,  and  consequentlythecostwill  be  greater;  the  manner  of  doing 
this  will  ije  explained  when  describing  a  12"  cylinder. 

To  prepare  the  staves  for  glueing,  first  see  that  they  are  out 
of  wind  on  the  face  1  2,  Fig.  .5;  then  dress  oif  on  one  edge  2  3,  to 
the  Ijevel  at  O,  then  gauge  for  the  width  2  1,  and  reduce  the  other 
edge  to  the  required  bevel.  After  the  staves  have  been  brought 
to  their  width,  make  a  cylinder  pattern  DBIl,  of  thin  stuff,  and 
mark  the  ends  to  the  curve  1,  2,  3,  then  with  the  cylinder  plane 
dress  down  to  tlie  curve. 

Where  the  stair-builder  is  favored  with  steam,  take  a  circular  saw 
havinj'  a  dia,nieter  not  over  the  diameter  of  cylinder,  to  use  as  a  wab- 
ble; tnen  place  a  guide  across  the  table,  held  down  with  two  hand 
screws,  now  run  the  staves  over  the  saw  several  times  until  leduced 
sufliciently  n-^ar  tlie  curve,  leaving  a  small  margin  for  a  guide  to 
keep  the  stuves  pirallel  wh'^n  glueing  them  up.  Also  if  having  a 
hand  .iointci ,  witli  an  adjustable  guide,  the  staves  may  be  reduced  to 
the  required  spiay,  thus  saving  much  time. 

Glueing.  For  good  work  the  glue  must  be  of  the  best 
grade,  and  carefully  prepared;  have  the  glue  so  that  it  will  run 
smooth  from  the  brush  without  any  lumps  or  being  stringy,  and 
the  hotter  the  better. 


Plate  22.  ^-^^ 

Rub  the  joint  \Yell  after  applying  the  glue,  to  lessen  the  thick- 
ness of  glue  in  the  joint;  now  set  the  "dogs,"  Fig.  8,  Plate  23, 
along  the  joint,  on  the  outside,  tapping  them  lightly  with  the 
hammer,  then  set  thom  away  to  dry;  afterwards  to  make  the  joints 
stronger,  screws  or  nails  may  be  used. 

If  there  is  .luy  sap  wood  on  the  joints,  rub  a  little  chalk  over  the 
SHp  part  before  applyiusr  the  glue  to  preveut  the  sap  wood  froni 
jib-iorbing  the  glue  too  fast.  For  all  light  work  the  doa:  will  be  found 
convenient;  with  their  use,  the  staves  for  large  cylinders  may  all  be 
glued  up  with  one  heating  of  the  glue. 

Dress  out  the  cylinder  to  the  pattern  with  the  "cylinder 
plane,"  then  see  that  the  two  joints  are  out  of  wind,  using  the 
winding  strips,  or  over  the  hand  jointer,  if  one  is  at  hand. 

Fig.  10.    Shows  plan  of  cylinder  and  the  strings  Joining. 

Fig.  11.  Slwivs  the  same  in  elevation.  The  joints  AB 
and  CD  are  reduced  to  the  thickness  of  strings  [f  ];  take  the 
cylinder  square  (that  is,  a  right  angle  triangle,  similar  to  the 
pitch-board.  Fig.  6,  made  from  pasteboard),  and  square  the  top 
line  BD,  from  the  etli^e  BA;  make  BF  equal  the  heighth  of  a 
rise  ["''l,  make  J'A  equal  DE,  Fig  7  [S^^j;  then  BA  will  equal 
[T^'-h8^'=l5'^]  15'^;  makeUCequal  DH.  Fig.  S  [T'H;  now  take  a 
thin  pliable  strip,  bend  it  into  the  cylinder  to  cbe  points  A  and  C. 
let  the  ends  of  strip  extend  out  from  the  joint,  tack  oxie  end,  and 
hokl  the  other  inider  the  thumb,  then  apply  the  pitch-board  to  the 
joint  of  cylinder,  and  regulate  the  ends  of  strip  to  the  pitch  by 
raising  or  lowering  that  part  of  strip  in  the  cyMader;  when  satis- 
factory, trace  the  falling  line  of  cylinder  with  a  lead  peacil,  and 
trim  off  the  surplus  wood  as  shown  at  Fig.  1 1.  The  shaded  part 
shows  the  cut  and  also  the  plough  on  the  face  of  joint  to  receive 
the  tongues  on  the  strings;  the  dotted  lines  show  the  staves  as 
glued  up. 

Now,  after  the  cylinder  is  fit  on  the  sti'ings,  and  the  lower  edge 
moulded,  glue  and  nail  the  cylinder  to  the  lower  string,  square  to 
the  face,  tack  a  brace  on,  to  hold  the  cylinder  firm;  cover  ail  ex- 
posed joints  so  as  to  protect  them. 

Dimensions  for  jointing  the  rail  on  the  bench. 

Next,  take  the  lengths  off  the  strings,  for  jointing  the  rail, 
and  enter  them  in  the  order  book,  to  be  used  when  getting  out  the 
rail. 

At  Fig.  7  the  first  length  is  shown,  taken  from  the  joint  GH, 
along  the  guage  line  to  the  cylinder  joint  at  the  point 2)  [11'',  8''''], 

At  Fig.  8  the  length  is  sliown  taken  from  the  joint  of  cylinder 
at  H,  along  the  guage  line  BC,  to  p  umb  with  the  face  of  No,  18 
rise  [2^  11%''], 

The  level  lengths  must  be  taken  at  the  building  and  after' 
wards  entered  in  the  order  book,  , 

Figs.  12,  13,  14.    Shoivs  plan  of  cylinder  and  elevation 

of  stHngs. 

In  this  case  the  strings  are  IK  thick,  and  halved  out  to  suit 
the  sides  of  cylinder;  the  cylinder  is  made  fast  by  screws  driven 
from  the  back  of  string,  sufficiently  slanting  to  draw  the  joint 
close  after  being  glued.  This  method  makes  a  good  firm  job,  but 
requires  more  time. 

f^~.  The  other  method  described  above  can  all  be  done  on  the 
shaping  machine,  where  steam  power  is  used. 

Preparing  the  steps  and  risers.  The  steps  and  risers 
will  be  next  in  order;  take  a  rod,  say  half  the  width  of  hall 
[3',  1'']  in  length,  set  off  from  right  to  left  3}i^^  for  the  radius 


104  Plate  23. 

of  eyHud<>r:  then  measure  to  the  right  '4''^  for  bracket:  then  l^^^ 
for  the  uosiDg  [3',  V^—S';4^^-i-}4^^~]-^i''-='y,  11"J  equals  2^  IV 
for  the  length  to  cut  the  steps  in  the  rough;  for  the  risers  they 
may  he  cut  the  thickness  of  nosing  [li"^'^]  less,  or  2^,  9yi^^'i  no 
allowance  has  been  made  for  squarhig  the  risers;  as  the  length  of 
steps  has  been  taken  between  the  rough  walls,  and  the  face  of  wall 
string  projects  out  \J4'^  for  base,  lath  and  plastering,  the  steps  are 
housed  %^^  into  the  wall  strings,  leaving  then  l}o^^  for  squaring 
the  ends  and  for  \nievcn  walls. 

Now,  there  are  18  risers,  the  rise  No.  1  and  No.  1.5  starting 
both  flights,  will  be  the  thickness  of  step  {IK''\  narrower  than 
the  rest;  there  will  be  two  landing  steps  8'^  wide;  the  one  at  the 
])latform  will  extend  across  the  platform  having  the  well  hole  cut 
outi  to  Q]4'^  diameter  to  receive  the  thickness  of  bracket;  the 
other  will  be  the  regu  ar  length. 

Then  again,  Nos.  1,  2  and  15  steps  will  be  2''^  longer  than  the 
regular  length;  that  will  leave  13  steps  that  will  cut  off  to  the 
regidar  length.  And  the  two  landings  deducted  otf  the  whole 
number  w^ill  leave  Itt  steps  that  will  re(iuire  to  be  the  full  width. 

Now  after  the  steps  and  risers  are  cut  otf  to  their  proper 
lengths,  size  thera  to  width;  the  width  for  the  regular  risers  will 
be  the  true  height  of  rise  1'^  plus  %'^  for  tongue  equals  T^g'''^.  see 
Fig.  .3,  Plate  23. 

The  width  of  steps  will  be  equal  to  the  tread  [10^^]  plus  %'^ 
for  tongue,  at  the  internal  angle  B,  and  plus  the  thickue.ss  of 
s-tep  1  )i^'  for  the  projection  of  nosing,  tinis  :  W -\-%'' ^l}i''  =^ 
n%'\  equals  U%  for  the  full  width  of  treads,  see  Fig.  3,  Plate 
23.  After  the  steps  and  risers  are  grooved  and  tongued,  cut  the 
miter  on  the  steps  for  the  return  nosings;  for  a  handy  means,  use 
the  miter  jack,  Fig.  7,  Plate  23. 

The  risers  should  be  grooved  so  as  to  allow  the  rise  to  be  a 
little  full  in  width,  so  that  when  keying  up  they  may  be  forced  up 
tight;  nothing  but  dry  stuff  diould  be  used  in  the  manufacture  of 
stair  work,  as  unseasoned  material  will  be  sure  to  give  trouble. 

Next  square  the  ends  of  the  risers  for  a  right  hand  rail,  then 
shoulder  back  }i^^  for  the  thickness  of  bracket  [k'^'J  pius  V  for 
th-Mhickness  of  string,  [}i''-+-V—\'^4:"\  equals  Di^',  as  showu 
at  A,  Fig.  4,  then  miter  the  ends  of  risers  to  receive  the  brackets. 

For  the  "platform  step"  use  the  platform  pattern  for  a  1'^ 
cylinder,  see  Fig,  10,  Plate  23.  With  this  pattern  mark  off  the 
miter  and  the  circular  part  to  be  sawed  out,  also  the  notch  for  the 
string  off  the  platform. 

The  stair  builder  will  find  the  above  pattern  answers  a  good 
purpose;  the  'circular  end  steps"  at  the  turnout  and  how  to  find 
their  location  is  shown  at  Figs.  1  and  3,  Plate  24. 

T^ig.  4.  The  dovetails  may  now  be  laid  off  on  the  ends  of  steps, 
and  also  ou  the  top  at  the  same  time;  the  balusters  are  2^''  square, 
the  center  of  baluster  should  be  the  center  of  dovetail;  then  take 
the  dovetail  pattern  and  make  from  the  guide  to  center  of  first 
dovetail  lli'^  for  the  projection  of  nosing,  and  V  more  to  center 
of  baluster,  equals  2  Vj^^',  thence  to  the  center  of  next,  the  dist.ince 
of  half  a  tread,  5^^  in  this  case. 

To  facilitate  the  oiieratiou  of  cutting  in  the  dovetail  on  the 
steps,  string  them  alon:;side  of  llie  bench,  all  face  out,  mark  and 
rip  them  in  to  the  proper  distance.  Now  stock  them  on  the 
trestles  and  mortise  tlit-ui  half  through  ou  the  biick,  leaving  the 
core  remaining  to  keep  the  mortise  clean  so  the  glue  will  adhere 
when  glueing  in  the  balusters. 


Plate  33.  luo 

Where  there  Is  steam  power  the  dovetails  may  be  cut  in 
uicely  on  the  band  saw  by  liaving  a  beveled  blocli  to  cant  tlie  step 
to  the  splay  of  mortise. 

Plaoe  the  short  baluster  with  the  two  faces  on  line  with  the 
fai-.i  of  rise,  and  also  the  face  of  bracket,  or  end  of  step,  as  shown 
at  A  and  X.  For  the  circular  end  steps  have  a  single  pattern, 
with  the  size  of  mortise  on  top  of  the  step  tacked  on,  so  that 
the  mortise  can  be  marked  on  top  of  the  step,  and  also  on  the  end, 
at  the  same  time. 

Glueing  up  the  step  and  rise.  Have  the  glue  not  loo 
thin,  place  the  step  on  the  bench  face  down,  glue  the  rise  in  phice. 
beiug  careful  to  keep  the  miter  on  rise  in  line  with  the  miter  on 
step;  glue  and  nail  tin- triangular  blocks  in  the  internal  angle  of 
step  and  rise.  .See  .B,  Fig.  3,  Plate  28.  Xow  glue  and  nail 
scotiu  D  into  place;  use  the  pitch-board  in  the  angle  of  step  and 
rise  to  keep  them  square;  sponge  olf  all  surplus  glue  from  the  face 
side  of  step  anil  rise,  and  lay  away  to  dry. 

Sometimes,  as  in  oak,  the  step  may  be  bowed  and  difficult  to 
glue  up.  They  may  be  mamiged  in  this  way:  Have  a  stout 
Ijench  top,  and,  with  two  hand  scrcv>s,  draw  liiy  lise  and  step 
down  to  the  bench  top,  then  block  and  nail  (he  ri:^e  to  place. 

Nosing  the  steps.  After  the  glue  is  dry  the  nosings  and 
scotias  may  be  Avorked,  being  careful  to  have  them  all  aliice.  In 
using  tlie  ''nosing  plane"'  work  down  to  the  round,  being  par- 
ticular of  the  last  shaving.  This  is  done  that  they  may  fit  snug 
in  the  housings. 

Panel  under  the  first  flight,  Fig.  1.  The  triangular 
panel  termiiiiiles  in  tliis  case  at  the  joint  of  cylinder,  and  extends 
up  back  of  the  string  J<";  find  the  starting  point  A,  say  plumb 
witli  the  face  of  second  rise,  then  count  the  uu)nber  of  full 
treads  from  A  t(i  joint  of  cylinder.  There  are  11  full  treads  at 
10'^  each,  and  the  last  tread  e.xteuds  into  the  cylinder  I",  leaving 
9>"  to  be  counted  into  the  pane!;  the  total  [11><10'^H'9'^=119^'--^^ 
W'—'i'.  \\"\  equals  9',  li'^  from  A  to  C,  along  the  floor. 

Now  make  a  scale  drawing  V  ',''  to  the  foot;  make  AC  equal 
9'.  11'^;  draw  a  i)erpendicu!ar  from  C,  then  place  the  point  of 
pitch-ljoard  at  A,  with  the  tread  along  the  liue  AC,  and  draw  the 
hypothcnuse  cutting  the  ijcrpendicular  from  C  at  D;  divide  the 
right  angle  triangle  ACD  into  panels  to  suit  the  fancy. 

Brackets.  For  ornamenting,  the  front  strings  are  usually 
yi'^  thick,  made  to  fancy;  they  are  mitered  to  t he  rise  for  good 
work,  and  the  nosing  returns  at  the  end;  those  for  the  cylinder 
may  be  cut  having  the  grain  of  wood  perpendicular  to  the  tread, 
then  steaming  and  bending  them  over  a  heated  stove  pipe  to  the 
required  curvature;  or  they  may  be  kerfed  on  the  back  and  sprung 
into  place. 

Circular  Nosings.  Are  worked  from  the  solid  including 
the  scotia:  the  scotia  is  sometimes  worked  separate,  and  each 
nailed  to  place  in  its  turn;  they  also  may  be  lurued  in  the  lathe 
for  small  cylinders. 

Return  Nosings.  Are  cut  a  shade  longer  between  the 
heels  of  miters  than  the  length  of  brackets,*  to  allow  for  smooth- 

*Thc  lii-ackets  are  usually  cut  '^"  lonucr  <hnn  the  width  of  tread: 
when  fillets  ai-e  used  the  lillet  lor  the  rise  is  mostly  1"  wide,  then  the 
uosing  is  cut  one  im-li  longer  tliau  tiic  v.idrli  of  tlie  tread  to  return 
around  the  fillet.  Souictimes  the  brackets  are  made  continuous,  and 
the  nosings  return  oa  themselves  ou  top  of  tho  brackets. 


106  Plate  22. 

Ing  the  joints;  for  good  work  the  returns  should  be  sized,  then  fit 
and  glued,  and  may  be  cleaned  off  at  the  bench. 

Building  up  the  stairs.  The  "well"' is  supposed  to  be 
trimmed  to  the  dimensious  laid  down  already  at  Fi^.  1,  and  the 
platform  framed  to  the  required  width  [3'',  0^^].  and  set  to  the 
proper  height  (8',  1").  from  top  to  top  of  joist  or  floor. 

Now  elevate  the  two  wall  strings  to  their  places  temporarily, 
to  see  if  they  are  correct  and  that  the  platform  is  in  the  proper 
place,  if  so,  then  select  three  long  scantling  for  bearers,  the 
straightest  one  to  come  against  the  front  string:  lav  them  on  the 
trestles,  place  the  front  string  on  the  scantling  selected  for  the 
outer  string,  keep  the  scantling  %"  back  from  liie  lower  edge  of 
string  for  the  lath  and  plaster;  mark  and  cut  the  upper  and  lower 
ends  of  scantling,  and  also  the  two  others  to  the  same  length,  and 
cut;  now  nail  the  string  to  the  scantling  and  elevate  the  same  to 
place,  keeping  the  center  of  cj'linder  to  the  center  of  hall  at  the 
platform,  and  the  face  of  string  at  the  lower  end  Z%"  from  the 
center  of  hall. 

Now  drop  a  plumb  line  from  the  face  of  trimming  at  AandB 
Fig.  l.to  see  if  the  proper  allowance  (8'''),  for  the  cylinder,  and 
thickness  of  level  fascia  is  correct.  Also  see  that  the  top  of  cylin- 
der is  down  from  the  top  of  platform  \i"  for  the  thickness  of  step, 
that  is  greater  than  the  thickness  of  floor;  when  all  is  correct, 
fasten  temporarily  at  the  bottom  and  also  at  the  piatforni,  then  see 
if  the  string  is  plumb  on  the  face  and  at  the  cylinder,  if  sd,  nail 
well  at  the  floor  and  at  the  platform,  try  the  plumb  again,  if 
found  all  right,  then  nail  up  the  middle  scantling  to  line  with  the 
first;  by  tacking  on  a  few  strips  to  the  two  scantling  they  will 
facilitate  getting  up  and  down. 

Squaring  the  wall  string  from  the  face  string.  The 
front  string  is  now  supposed  to  be  set  straight  and  plumb  on  its 
face;  select  two  or  three  steps  and  risers,  cut  them  off  long 
enough  to  enter  the  wall  string  and  project  over  the  face  string 
J4'^  to  receive  the  brackets,  place  them  in  the  wall  string  at 
different  points  and  wedge  them  slightly,  then  move  the  wall 
string  in  or  out  as  required  to  bring  the  steps  square  with 
the  face  string  to  receive  the  brackets;  when  found  square 
and  level,  make  a  mark  on  the  floor  at  No.  1  rise,  also  with 
chalk  mark  for  the  plugs  (if  brick  walls)  at  several  of  the 
housings  and  along  the  upper  edge;  now  remove  the  string  and 
plug  the  walls,  then  reset  the  string  to  place,  keeping  the  face 
of  string  XJi"  from  the  wall  to  allow  for  plastering  and  the  thick- 
ness of  base;  nail  through  the  housings  so  that  few  nails  may  be 
seen  as  possible;  before  the  wall  string  is  nailed  the  landing  (u- 
platform  step  should  be  cut  to  length  and  entered  in  place. 

Now  cut  and  put  in  the  steps,  beginning  at  the  top  and  stop- 
ping down  from  the  platform;  when  the  steps  to  the  platform  are 
cut  and  in  place,  then  proceed  to  set  the  strings  for  the  short  flight 
off  the  platform.  Elevate  the  face  string  from  the  cylintler,  keep- 
ing the  upper  end  at  M,  lig.  8,  even  wiih  the  Joist;  then  fasten  the 
string  temporarily.  tSee  that  the  step  at  the  landing  will  come 
level;  also  see  if  there  is  the  proper  distance  \j"\  between  the 
strings  at  the  point  jB,  Fig.  1;  if  so,  tiien  glue  the  joint  at  cylin- 
der and  nail  up  firm  at  'B;  next  cut  in  and  nail  the  bearers  to 
the  platform,  landing  joist  and  front  string,  keeping  the  bearer 
up  the  %"  from  the  lower  edge,  for  lath  and  plastering,  then 
nail  up  the  middle  bearer  and  square  the  wall  string.  Cut  and 
put  in  the  steps  as  before. 


Plate  23.  107 

Kow  proceed  to  glue  in  the  wedges.  Have  the  glue  for  this 
job  thicker  tlian  for  ordinary  work.  Begin  to  wedge  from  above, 
wedge  up  the  rise  first,  tlieu  the  step  that  is  glued  to  the  same 
rise.  Two  persons  should  help  at  this  work,  one  above  with  ham- 
mer and  block,  tappiug  the  step.  This  helps  the  step  and  rise  to 
come  up  close  at  the  nosing  and  scotia. 

After  the  steps  are  all  wedged  up,  set  and  nail  the  scantling 
at  the  walls  to  receive  the  lath.  Where  the  scantling  comes  against 
stud  partitions,  keep  the  bearer  out  from  the  partition  to  allow 
the  lathing  on  the  partition  to  pass  behind  the  bearer.  Then  cut 
rough  brackets,  as  shown  at  E,  Fig.  2,  having  the  grain  of  wood 
vertical  or  perpendicular  to  the  treads.  They  should  be  equal  to 
a  tread  in  width  (10^^).  Keep  them  }i^'  above  the  lower  edge  of 
bearer,  as  shown.  This  is  done  in  case  there  is  auy  shrinkage  of 
timber  the  plastering  will  not  be  injured  by  the  ends  of  braclvets. 

After  this  cover  the  steps  with  rough  boards  to  protect  the 
steps  while  plastering.  Put  up  the  level  fascia  ami  }-i  cylinder, 
allowing  the  same  to  project  down  Ji^^  below  the  joist  to  receive 
the  lath  and  plaster;  then  put  in  the  triangular  panel:  also,  cut  in 
a  block,  2^,  6^'  high  from  floor  to  center,  to  receive  the  wall 
rosette  at  the  upper  end  of  hand  rail,  and  also  at  K  aud  F,  Fig.  2, 
for  solid  nailing  when  putting  down  the  base,  mouldings  and 
easements. 

Now  take  the  lengths  of  rail  along  the  level  from  the  face  of 
landing  rise  to  joint  of  }%  circle,  as  CH  in  elevation,  Fig.  2, 
(5^  6>.£^0;  then  from  H  circle  to  wall  (3^  V)  on  plan  Fig.  1. 
These  lengths  enter  in  the  order  book  when  returned  to  the  shop. 


PLATE  23. 

Plate  23.  (Scale  %'''— 1  foot).  Exhibits  the  steps  and 
rf-sers  mid  vianner  of  constructing  the  scone;  aUo,  how  the  steps 
are  sxipported  underneath. 

Fig.  1.  Shows  the  elevation  of  Oirce  steps  at  the  slatting 
of  Fi<j.  1,  Plate  22. 

AA  shows  the  steps  tongued  into  the  rise,  and  giooved  on 
the  umlerside  to  lecelve  the  tongue  on  the  risers  C,  C,  C.  At 
D,  D,  D  is  shown  the  scotias;  at  F  the  bearer  is  shown  cut  olf  to 
suit  the  floor;  .£7  shows  a  rouj,h  bracket  nailed  to  the  bearer,  and 
through  the  rise  into  the  step;  the  bracket  is  shown  cut  off  a  little 
above  the  lower  eilge  of  bearer  to  prevent  damage  to  the  plaster 
in  case  of  shriukage.  The  grain  of  wood  should  be  perpendicular 
to  the  tread. 

Fig.  2.  Sliows  the  upper  end  of  flight  landing  on  the 
platform;  also;  the  short  flight  staHing  off  the  same  and  landing 
on  the  second  tioor. 

AAA  shows  the  full  step;  C,  C.  Cthe  risers:  BB  the  blocks 
glued  aud  nailed  iu  the  internal  angle  of  step  and  rise,  on  the 
umlerside,  to  give  strength  aud  pievent  squeaking;  DD,  the 
scotias,  H^''  by  J4'^  for  1  }i'^  stei)S,  and  %^^  by  V^  for  13-4^^  steps: 
i^JF*  shows  the  bearers  fit  up  to  the  joist  HH  nt  the  platform  and 
landing;  the  upper  bearer  is  shown  "bird-mouthed"  on  to  a  cleat 
at  tlie  lower  end;  EE  shows  the  rough  brackets  nailed  to  the 
bearers,  having  blocks  J  J  glued  and  nailed  iu  the  angles  of  tread, 
rise  and  bracket;  in  this  case  the  brackets  must  be  made  from 
dressed  lumber. 


108  Platk  23. 

At  K  and  i  the  platform  and  landing  steps  are  sized  down 
on  the  joist  to  agree  with  the  thicliuess  of  floorinj;:. 

Fig.  3.  Shows  a  step  and '1-1-96  to  a  larger  scale.  (\]4''-=\ 
foot). 

A  shows  step  \}4''  thick,  and  the  nosing  projecting  1^'^; 
the  rise  is  7^^,  and  tread  W. 

Fig.  4.  Shows  the  scotia  D  fit  into  a.  gioove  In  the  step  A, 
a)t(l  the  riser  C  to  coinein  behind,  to  he glned,  bJoclied  and  nailed. 
The  former  method.  Figs.  2  and  :;,  will  give  more  wear,  as 
ihe  groove  for  the  latter  method  cuts  into  tlie  projecting  nosing, 
leaving  less  solid  wood  to  be  worn  away,  but  is  the  method  usually 
adopted. 

Fig.  5.  Shows  the  step  extended  to  the  bach  of  rise,  and  the 
rise  tontjnvd  down  into  the  step. 

This  method  is  more  convenient  when  stepping  up  winders, 
as  the  stepping  up  is  started  from  below  instead  of  above,  as 
shown  at  Fig.  3.  More  satisfaction,  and  abetter  job,  can  be  made 
by  the  former  method. 

If  the  groove  in  the  step  at  the  internal  angle  A  be  the  least 
open  it  shows,  and  will  catch  and  hold  the  water;  then  again,  in 
nailing  up  through  the  step  into  the  rise,  on  the  underside,  there 
is  more  dansier  of  splitting  the  step  along  the  groove:  and  also, 
wider  stuff  is  required  for  the  steps. 

Fig.  6.  Shows  the  manner  of  sliouldering  and  mitering  the 
rise  Cto  suit  the  thickness  of  string  D;  the  miter  is  shown  at  A. 
Where  there  is  steam  power  the  tennon  machine  does  the  shoulder- 
ing and  mitering  both  at  the  same  time,  neat  and  speedy. 

Fig.  7.  Slwios  the  miter  templet  for  mitering  the  ends  of 
steps  for  Vie  return  nosings. 

S  sliows  the  step:  B  the  box,  the  sides  so  set  as  to  take  in  the 
tliickness  of  step  ea.-^ily;  A  is  a  stop  to  come  up  to  the  end  of  step; 
iOf  is  the  miter,  and  B  .showsaguage  line  run  on  the  side  of  box 
a.s  a  guide  lor  the  saw.  In  a  hand  shop  this  templet  will  be  found 
convenient:  use  a  guard  on  the  back  saw  for  the  reqiiired  depth. 

Fig.  8.  Shows  the  "dog,"'  made  from  steel  f^'^  square,  for 
bench  use.  They  should  be  heavier  at  the  center,  and  dra\ATi  out 
gradually  at  the  points;  they  should  taper  slightly  on  the  inside 
towards  the  point  of  tusks,  so  that  when  driven  they  will  grad- 
ually bite  the  harder.  If  the  taper  is  too  great  they  will  spring 
out  in  hard  Avood. 

Fig.  9.  [Scale  )^^^=-l  foot].  Shows  the  size  of  bearer  re- 
(piired  under  a  flight  of  15  risers,  straight  run,  so  as  not  to  de- 
llcct  over  .03  of  an  incTi  per  line(U  foot. 

The  length  of  bearer  SB  is  1.5^,  0^\  from  the  joist  starting  to 
the  joist  landing:  the  liorizontal  distance  KL  between  the  joist 
starting  and  landing  is  11.''  2^'';  DD  shows  two  timbers  4'''  by  .5'' 
flit^hert  with  a  %^^  by  4^''^  iron  plate,  bolted  together;  at  S  is 
shown  an  iron  "stirrup."  forming  a  "shoe"  for  the  lower  end  of 
bearer;  CC  shows  the  trimmers,  above  and  below;  EF  shows  the 
face  string;  iirff  the  lower  edee  of  .same,  or  line  of  plastering; 
W  shows  the  weight.  The  formula  to  find  the  size  of  material 
required  is  explained  at  the  end  of  letter  press  for  Plate  28. 

Fig.  10.  Slioirs  a  circular  step  pattern  to  mark  off  the 
platf&rni  step  for  a  1"  cylinder. 

The  face  of  rise  No.  14  and  15  is  in  the  cylinder  X^\  as 
shown;  the  radius  is  3J4''";  at  A  a  hole  is  shown  to  hang  the  pat- 
tern up.  In  a  shop  doing  a  large  business  a  set  of  these  patteras 
for  the  different  cylinders  will  be  found  very  economical. 


ri.AiK  24.  109 


PLATE  24. 

Plate  24.  (Scale,  l}ij^^=^l  foot).  ExhiMts  the  construction 
of  face-moulds  for  the  stuir-case,  Piute  22,  Tlw  holustei's  are  2" 
yC^i" ;  rail  i'^  u^klc  X  2}4^^  deep,  and  newel  7^'  <  '<";  the  pit)-h  is 

Fig  1  and  2.  Sltoivs  lion  to  place  the  risers  and  Jiiid- 
ftte  radius  of  turiiout  at  the  newel  post. 

Draw  the  base  line  AB,  Fig:.  2,  elevate  No.  1 ,  2  and  ."  risers 
and  treads;  through  the  center  of  balusters  XX,  draw  the  inclina- 
tion of  the  under  side  of  rail.  Parallel  witli  XX  draw  the  center 
of  rail  DC  indefinite;  from  the  top  of  No.  1  step  set  up  4>2^' 
t6  the  under  side  of  rail  for  the  difference  that  the  newel  is  longer 
than  a  short  baluster;  for  example  say  the  short  baluster  is  •?/,  2^^ 
from  the  top  of  first  step  to  the  underside  of  rail  at  the  center  of 
the  baluster,  then  the  newel  post  will  be  ry-^-^plus  4)4^',  or  2^, 
63^''^  high  from  top  of  step  to  the  under  side  of  rail. 

Then  make  JE?!^ equal  4K^'  and  FG  eqnallJi''^  to  the  center 
of  rail:  from  G,  and  parallel  to  AB,  draw  CiT  indefinite,  cutting 
the  inclination  of  the  center  line  of  rail  DC  prolonged,  at  iif. 
From  H,  and  perpendicular  to  AB,  draw  HB,  to  Fig.  1.  Draw 
BC  indefinite  and  parallel  to  AB,  to  indicate  the  center  of  rail  on 
plan,  Fig.  1;  draw  No.  1,  2  and  3  rise  opposite  those  at  Fig.  2: 
place  the  center  of  newel  post  on  line  with  the  face  of  No.  1  rise, 
and  out  any  distance  from  the  center  of  rail  that  may  be  desired, 
say  in  this  case,  as  the  hall  is  narrow,  we  place  the  side  of  newel 
to  line  with  the  back  of  balusters;  then  the  center  of  newel  at  O 
will  be  out  from  the  center  of  baluster  2i4''^;  draw  OB,  draw  the 
size  of  cap,  cutting  OB  at  H.  Make  HD  equal  half  width  of 
rail  [2"]  for  the  point  of  miter,*  make  BC  equal  BD,  then  BD 
and  BC  are  the  tangents  on  plan.  From  C,  and  perpendicular  to 
tangent  BC,  draw  CE  indefinite;  also  from  D,  and  at  right 
angles  to  tangent  BD,  draw  DF  prolonged  to  intersect  CE,  (for 
want  of  room  ncit  shown).  Make  CK  etiual  %^^  for  the  face  of 
string;  make  KL  equal  K''''  for  the  face  of  bracket;  also  make 
JjJH"  equal  IJ^'''  for  the  projection  of  iiosiug.  From  the  intersec- 
tion (not  shown),  draw  the  curve  of  turnout  through  the  point  K, 
for  the  cylinder,  shown  by  the  solid  line;  also  draw  the  bracket 
and  nosing  lines.  Now  draw  the  risers  to  intersect  the  bracket 
line,  and  the  projection  of  the  nosings  to  intersect  the  nosing  line; 
then  through  the  intersections  draw  the  miters,  thus  locating  the 
risers  aud  treads  and  the  radius  lor  the  turnout  at  newel  post. 

This  drawing  should  be  male  on  paper  to  prepare  the  steps 
and  risers,  also  the  cylinder;  afterwards  rolled  up  until  the  rail  is 
wanted,  then  the  drawing  may  be  completed  for  the  conslnictiou 
of  the  face-mould. 

Pigs.  1,  2,  3  and  4.  Show  the  construction  of  face 
mould  for  the  turnout  at  the  neioel  post. 

The  position  of  newel  post,  location  of  risers  in  the  cylinder, 
tangents,  and  location  of  the  first  rise  [No.  3]  outside  the  spring 
of  cylinder  are  shown  [r>^^]  on  plan  Fig.  1.  This,  together  with 
so  much  of  the  elevation.  Fig.  2.  as  the  base  Hue,  the  elevation  of 
treads  and  risers,  and  the  inclinati(jn  of  the  center  line  of  rail, 


*Some  prefer  to  extend  the  curve  of  turnout  to  the  point  of  miter 
as  here  described,  instead  of  termiuatliig  the  curve  at  the  intersec- 
tion of  cap,  and  adding  on  straight  wood  for  the  miter  as  shown  at 
Figs.  12  and  14,  Plate  29.  By  carrying  the  curve  to  the  point  of  miter, 
and  moulding  th«  wreath-piece  to  suit  the  cap,  gives  the  best  results. 


110  Plate  24. 

has  been  explained.  The  drawing,  it  is  supposed,  has  been  made 
on  paper  and  laid  away  until  the  rail  is  wanted.  Now,  to  prevent 
a  confusion  of  lines  on  plan  Fig.  1,  we  will  make  another  plan. 
Fig.  3.  Draw  the  tangents  DJ3  and  JSCto  correspond  in  length 
with  tangents  on  plan  Fig.  1,  and  also  in  the  angle  at  J3;  D  2  and 
D  3  show  the  miter  into  the  cap;  DF  and  CJ57  indicate  the  radial 
lines.     [For  want  of  room  their  intersection  is  not  shown]. 

Now,  parallel  with  DB  and  BC  draw  DH  and  CH  for  the 
parallelogram  HDBC  on  plan;  prolong  the  tangent  BC  towards 
K  for  the  direction  of  siraiglit  rail;  from  D,  and  at  right  angles 
to  CB  prolonged,  draw  DJ;  join  CD  for  the  chord  on  plan; 
draw  the  diagonal  BH;  cutting  Ihe  short  chord  at  4,  draw  the 
curve  CD  for  the  center  line  of  rail  on  plan.  Draw  the  width 
of  rail  as  shown. 

Now,  at  Fig.  1,  draw  the  radial  line  EC  on  plan  perpendicit- 
lar  to  AB,  cutting  the  inclination  of  the  center  of  rail  at  N\n 
elevation;  prolong  GH to  cut  CiV" at  K,  then  KN  will  equal  the 
height  that  the  wreath-piece  has  to  raise,  and  UN  will  be  the 
length  of  tangent  in  elevation. 

Make  K  2  equal  the  chord  DC,  Fig.  3;  make  K  6  equal  the 
diagonal  BH,  on  plan  Fig.  3;  join  N  2:  make  H  4  equal  BJ, 
Fig.  3;  from  4  and  perpendicular  to  NH  prolonged  draw  4  5. 
Make  joint  at  D  plumb  over  No.  3  rise  and  perpendicular  to  the 
inclination  DH. 

Fig.  4.     SJiorrs  the  face-mould  for  the  turnout. 

At  any  convenient  place  on  the  paper  for  face-mould,  draw 
BC,  with  Cas  a  center,  and  iV2,  Fig,  2,  for  a  radius;  draw  arc 
at  D;  then  with  BD,  Fig.  3.  as  a  radius,  and  B  for  a  center, 
draw  arc  intersecting  at  D.  Join  BD,  draw  DO  and  CO  parallel 
with  BC  and  BD  for  the  parallelogram  ODBC  on  the  cutting 
plane,  or  plane  of  plank. 

Proof.  The  diagonal  HO  must  equal  the  distance  N  6,  Fig. 
2;  if  so,  the  angle  of  tangents  at  B  is  correct. 

Prolong  tangent  BC  6^'  to  E;  make  joints  at  D  and  JE7  per- 
pendicular to  the  tangents  BD  and  BE. 

Bevels.  To  find  the  bevels  return  to  Fig.  2.  Suppose  the 
base  line  AB,  Fig.  2,  to  be  the  edge  of  draught-board;  at  any 
convenient  distance  over  draw  a  gauge-line  7  8;  perpendicular  to 
AB  draw  PR  equal  to  DJ,  Fig.  3;  make  P  9  equal  4  5;  make  P 
10  equal  the  height  KN;  draw  R  9  and  JE  10  prolonged  to  edge 
of  board,  then  the  angles  at  9  and  10  give  the  bevels  required. 
Parallel  witli  7  8  draw  the  half  width  of  rail  as  1  12,  cutting  the 
hypothenuse  of  bevels  at  13  and  14. 

PiCturn  to  Fig.  4.  Make  DM  and  D  13  each  equal  10  13,  Fis. 
2;  also,  make  JEiV^and  E 14  each  equal  9  14,  Fig.  2.  Make  C  T, 
Fig.  2,  equal  B  4,  Fig.  3;  from  T,  and  parallel  to  KN,  draw  TS, 
Fig.  2:  prolong  the  joint  DM,  and  also  the  diagonal  BO,  to  in- 
tersect each  other  (not  shown  on  plan),  and  from  the  intersection 
draw  KJ  indi'finite. 

Make  BF  equal  6  S,  Fig.  2,  join  FD.  From  13,  and  parallel 
with  DF,  draw  the  proportional  line  13  H,  cutting  OB  produced 
at  H;  make  FL  equal  FH;  from  N  and  14  draw  lines  parallel 
to  BE  to  intersect  the  radial  line  at  K  and  J. 

Now,  with  a  pliable  strip  applied  to  the  points  DFC,  draw 
the  curve  for  the  center  of  rail;  also,  through  the  points  13,  H, 
J,  trace  the  curve  for  the  convex  side  of  mould,  and  through  the 
pointsMLiT  trace  the  curve  for  the  concave  side  of  mould. 

At  sections  P  and  R  the  tangents  are  shown  carried  across  the 
joint  intersecting  the  g-auge-line.  The  hevel  found  in  the  angle  atlO, 
Fig.  2,  is  shown  applied  from  the  face  of  crook,  through  the  intersec- 


Plate  24.  Ill 

tlon.  In  like  manner,  the  bevel  found  In  the  angle  at  9,  Fl?r.  2,  Is  ap- 
plied at  section  R,  and  the  block  pattern  shows  the  twist  of  wreath- 
piece.  The  shaded  part  shows  the  amount  of  wood  required  to  saw 
out  the  crooks;  and  the  arcs,  shown  laid  ofif  from  the  center  line  on 
face  mould,  gives  the  lines  to  follow  when  sawing  out  the  crook  square 
through  the  plank.  Observe  the  bevels  do  not  cross  the  tangents  in 
their  application  In  this  case  because  the  minor  axis  is  not  in  the 
mould,  or  there  is  no  point  in  the  width  of  mould  that  is  equal  to  the 
true  width  of  rail  [4"1.  Hence  the  bevels  both  apply  the  same  way; 
also,  observe  the  steepest  bevel  is  applied  to  the  widest  end  of  mould. 
For  sliding  this  kind  of  a  mould  on  the  crook  see  Fig.  5,  Plate  10. 
Sight  holes  are  shown  on  the  face-mould  to  aid  in  adjusting  the  mould 
over  the  tangent  on  the  crook. 

Fig.  5.  SJimvs  plan  of  the  center  line  of  rail  for  a  1^'  cyl- 
inder, and  2"ys2"  balusters. 

The  radius  for  a  7^^  cylinder  will  equal  S14^^,  and  the  bracket 
equals  >4  ^''  in  thickness;  the  face  of  baluster  will  be  flush  with 
the  line  of  bracket,  and  hence  the  center  of  baluster  will  project 
%^''  beyond  the  line  of  cylinder,  making  the  radius  for  the  center 
line  of  rail  r3K^^+K''=4M''J  equal  4^'^ 

Draw  AJB  indefinite;  then  with  O  as  a  center,  and  OB 
[4.^^^]  for  a  radius,  draw  the  semi-circle  BCA,*  enclose  the  semi- 
circle with  the  rectilineal  parallelogram  ABDE;  draw  the  radius 
OC.  and  we  have  the  two  square  parallelograms  OBDC  and 
OCEA,  on  plan. 

Prolong  tangents  DB  and  EA  towards  M  and  N  for  the 
direction  of  straight  rail;  make  the  face  of  No.  13  and  14  rise 
93s''''  from  the  spring  of  cylinder  to  correspond  with  Fig.  4,  Plate 
22,  then  the  face  of  No.  14  and  15  rise  will  be  in  the  cylinder  )i^^. 

Fig.  6.    Shoivs  the  development  of  tangents. 

Let  XX  indicate  tlie  edge  of  drawing  board;  make  BD,  DC, 
CE  and  EA  equal  tangents  BD,  DC,  CE  and  EA  on  plan,  Fig. 
.5.  Through  B,  D,  C,  E  and  A  draw  perpendiculars  to  XX 
indefinite;  now  elevate  the  risers  and  treads,  keeping  the  face  of 
No.  13  and  16  rise  9)^^''  from  the  spring  lines  at  A  and  B:  (No. 
16  rise  not  .sliown),  through  tlie  center  of  baluster  JJ"  and  (S-S, 
draw  the  inclination  of  the  under  side  of  rail  parallel  with  the 
under  side  of  rail,  draw  the  center  line  of  rail,  cutting  the  perpen- 
diculars B  atid  D  at  G  and  H;  and  also  cutting  the  perpendicu- 
lars A  and  E  at  IT"  and  T:  loin  Ti?,  cutting  the  perpendicular 
from  C  at  K.  Parallel  with  XX,  draw  GL,  cutting  DH  at  3; 
parallel  ^vith  XX  diaw  KM,  cutting  Z>jFf  prolonged  at  3.  Now. 
LK  will  be  the  height  the  wreatli-piece  is  required  to  raise,  and 
as  LK  is  one-lialf  the  whole  height  around  the  semi-circle,  only 
one  face-mould  will  be  required. 

Prol<)iig  tangent  KH  to  intersect  BM  at  JV;  prolong  tangent 
GH  U)  intersect  MK  at  P;  fnnu  3.  and  at  right  angles  to  GP- 
draw  3  4;  fnuQ  2,  and  perpendicular  io  NK,  draw  2  5;  parallel 
with  DH.  draw  the  half  width  of  rail,  cutting  GH nt.  6,  and  KH 
at  7.  Make  GO  equal  the  clwrd  JSCou  plan.  Fig.  5.  A  squared 
section  of  rail  is  shown  at  Q, 

Joint  Bevels.  Parallel  with  XX  draw  the  dotted  line  8 
9:  draw  9  10  pvrpendicular  to  XX  and  equal  to  the  radius  OC. 
Fig.  .5.  Make  9  11  equal  3  4,  Fig.  6;  also,  make  9  13  equal  2  5, 
Fig.  6;  draw  10  12  and  10  11  prolonged  to  edge  of  board.  The 
bevel.>  are  shown  in  tiie  angles  at  11  and  12. 

Fig.  7.     Shows  the  face-mould. 

Make  GH  equal  GH,  Fig.  6;  with  G  as  a  center,  and  CM, 
Fig.  6,  for  a  radius,  draw  arc  atK;  again,  with  fi"  as  a  center,  and 
HK,  Fig.  6,  for  a  radius,  draw  arc  intersecting  at  K;  draw  HK; 
parallel  with  HG  and  JEfJTdraw  KG  and  GO  for  the  parallelo 
gram  OGHK  on  the  cutting  plane,  or  plane  of  plank. 


113  Platk  24, 

Pioof.  The  diagonal  OH  must  equal  ON,  Fig.  6;  if  So,  tlip 
angle  of  tangents  at  H  is  correct. 

Prolong  tangent  HG,  6"  to  F  for  length  of  shank;  make 
joints  at  J' and  iiC  at  right  angles  to  tlie  tangents;  prolong  OG 
and  Oif  indefinite;  make  G  5  and  G  6  p:ieh  tqual  H  7.  Fig.  0: 
also,  make  if  7  and  K  S  each  equal  H  C>,  V\g.  C;  make  GA  equal 
HP,  Fig.  6;  draw  OA  for  the  direction  of  minor  axis;  let  O  -.1 
equal  OC,  Fig.  1.  for  the  semi-minor  axis;  make  2  3  and  2  4  each 
equal  the  half  width  of  rail  [2"].  Draw  fi  10  and  .5  0  parallel  to 
GF  for  the  shank  of  mould.  Now  pivot  the  trammel  at  O  with 
the  arms  at  right  angles  to  the  minor  axis  as  shown.  Then  set 
from  pencil  on  rod  to  minor  pin  the  distance  O  i,  ])lace  the  pencil 
at  7,  drop  the  pins  in  the  grooves,  and  fasten  the  major  pin;  then 
trace  the  concave  side  of  mould  through  tlu>  jioints  «,  4,  7. 
Again,  set  from  pencil  to  minor  pin  the  distance  O  .3.  then  place 
the  pencil  in  ^,  drop  the  pins  in  tiie  grooves,  fasten  the  major 
pin,  and  trace  tlie  convex  sMc  of  mould  through  the  points  r>,  a,  S. 

At  section  .B  the  bevel  found  in  the  angle  at  11.  Fig.  G,  is 
shown  applied  through  the  center  of  plank;  at  secllou  C  the  bevel 
found  in  the  angle  at  12,  Fig.  6,  is  applied  in  the  same  manner. 

The  block  pattern  shows  the  squ.ii'e  serlion  of  rail;  the  shaded 
part  indicates  tlio  amount  of  over  wood  IIki;  Ins  to  be  removed  in  the 
formation  of  the  wreath-picco,  also  the  llii'-kiiess  of  plank  required 
for  the  twist,  [4"1.  In  many  cases  less  willr! o;  this  is  owing  to  Ihu 
style  of  rail,  as  the  corners  may  work  olf  or  I'-inain full 

If  a  trammel  is  not  at  liand,  draw  llie  two  right  angles  at  O.  and 
use  a  rod  iis  previously  described,  or  find  anotlier  point  on  the  diag- 
onal OH,  and  use  a  flexible  strip.  T)ie  poi.'it  on  the  diai^onal  OH  "is 
found  on  the  din yronal  OA' in  elevation  from  O  to  tlio  intersection  at. 
the  pcrpendicubir.  For  a  correct  face-mould  the  trammel  gives  the 
curves  absolutely  correct  foi  all  cylindric  soirtions  that  are  circular 
on  plan. 

Figs.  8  and  9.  Show  how  to  nppl]/  the  tang'iids  to  the 
crook  ojid  slide  the  mould. 

The  face-mould  at  Fig.  8.  is  made  from  '■.,''' stuff,  and  has  three 
holes  bored  through  on  the  tangents  for  siu'iit  holes  to  aid  in  slid- 
ing the  mould  over  the  tangents  on  the  crook.  The  heavj'  line 
XXXX,  Fig,  8,  shows  the  crook  sawed  out  \:>  a  parallel  width  and 
square  through  the  jdank. 

First  see  that  the  crook  is  out  of  wind  on  the  face  and  near 
a  uniform  thickness:  now  place  tlie  face-mould  in  the  center  of 
crook,  and  transfer  the  tangents  from  the  mould  to  the  crook,  as 
shown  by  the  heavy  dotted  lines  2  8  and  :'.  4.  Mark  the  joints 
X2  X  and  X  i  X;  then  cut  and  dress  off  the  joints  square  to  the 
tangents,  and  also  to  the  face  of  plank.  Now  cany  the 
tangents  across  the  joints  square  to  the  face;  then  mark  the 
tangents  on  the  opposite  side  of  crook.  Where  there  is  a  shank 
rt^'  or  6''''  long,  as  XA,  a  good  plan  is  to  joint  the  shank  XA 
square  to  the  face  of  crook,  then  run  a  gauge-line  on  for  the 
tangent  2  .3;  then  place  the  mould  to  this  line  and  mark  the 
tangent  3  4.  Then  tlie  shank  joint  cati  be  squared  from  the  face 
and  side  of  shank. 

Xow  center  the  joints  as  shown  at  sections  P  and  R  with  a 
gauge  .shown  by  the  dotted  lines  on  the  face  of  joints,  making 
both  centers  the  same  distance  from  the  face  of  crook. 

Next  apply  the  bevels  through  the  points  P  and  R;  then, 
from  where  the  bevels  cut  the  upper  and  lower  faces  of  crook,  as 
5  6  and  7  8,  draw  another  set  of  tangents  FH  and  HK  parallel 
to  2  3  oud  3  4;  repeat  the  operation  on  the  opposite  side  of  crook: 
these  last  lines  are  the  lines  on  which  the  mould  has  to  slide. 
Now  slide  the  face  mould  so  that  the  tangents  FH  and  HK  on 


fl,ATE   34.  113 

the  moiild  will  exactly  foincide  with  the  tangents  J'J3' and  iifiiC 
on  tlie  crook.  The  sitfht  holes  will  aid  in  locatins?  the  mould,  as 
shown.  Now  mark  around  the  mould  for  the  lines  to  dress  oft' 
the  overwood;  before  lifting  the  monld  transfer  the  minor  axis  0 
10  to  the  face  of  crook;  then  apply  the  mould  to  the  opposite  side 
in  the  same  way.  It  will  be  observed  that  at  B  an<l  X>  the  monld 
extends  beyond  the  crook,  and  the  lim;  for  wiv.kini?  off  to  the 
plnmb  will  be  lost,  while  on  the  opposite  side  the  line  will  show. 
A  good  plan  for  the  learner  in  this  case  will  l>e  to  tiick  the  mould 
in  its  place,  and  the  arris  of  mould  will  be  a  guide  to  work  off  the 
surplus  wood  to  the  plumb. 

Fig.  9.  Shows  the  crook  turned  up,  and  the  concave  aide 
is  shown  worked  off  to  the  plumb  lines. 

Two  patterns  are  here  shown  to  give  a  better  idea  how  the 
monld  is  applied.  One  pattern  is  all  that  is  required  iu  practice, 
lly  dressiug  down  the  coucave  side,  as  shown,  and  using  the 
(.'upper  gauge  shown  at  Fig.  \:l,  Plate  21.  the  convex  side  of 
wreath-piece  may  be  gauged  to  the  reijuired  width  without  the  aid 
of  face-mould.  As  the  bevels  are  applied  they  show  the  wreath- 
piece  intended  fora  right  hand  rail  and  laniling  on  the  platform; 
for  the  wreath-piece  off  the  platform  apply  the  bevels  the  reverse 
way  of  this;  or  it  will  be  seen  that  if  the  wreath-piece  be  turned 
face  down  it  will  answer  for  the  wreath-piece  off  the  platform. 

One  thing  the  beginner  must  remember;  that  is,  when  work- 
ing off  the  surplus  wood  to  the  plumb  he  must  hold  his  tools  near 
as  he  can  to  the  plumb.  The  minor  axis  that  is  marked  on  both 
sides  of  the  crook  will  be  the  direction  to  hold  the  tools,  as  9  0. 

After  the  crooks  have  been  dressed  to  the  phnnb  bevels  on  the 
concave  side,  then  bolt  them  together  at  the  center  joint,  keeping 
the  center  lines  on  the  joints  opposite  eacli  other.  Tlien  stand  the 
twist  on  the  floor  and  cast  the  eye  clown  on  the  concave  side  and 
see  if  the  curve  i.s  correct,  having  no  kinks  or  abrupt  places,  when 
all  is  satisfactory.  Then  use  the  Cupper  gauge  and  gauge  from 
the  concave  side  for  the  width  of  rail,  then  unbolt  and  dress  otf 
the  convex  side.  Then  bolt  them  together  again  and  dress  otf  at 
the  center  joint  carefully  that  the  two  wreath-pieces  may  join  each 
other  without  kinks.  Just  here  a  good  way  to  prove  the  correct- 
ness of  center  joint  is,  first,  see  that  the  center  lines  made  from 
the  bevel  are  exactly  opposite,  or  parallel  to,  each  other  when 
bolted  together.  Then  place  the  wreath  dov\-n  on  a  true  surface  on 
the  side,  as  shown  at  Fig.  9,  and  see  if  the  shank  of  upper  wreath- 
piece  is  parallel  with  the  true  surface;  if  so,  the  joint  is  correct. 
Again,  just  here,  the  wreath  for  a  platform  may  be  tested,  to  see 
if  the  shanks  have  the  right  direction  for  the  pitch  to  and  off  the 
platform,  by  laying  down  the  Inclination  of  the  pitch  to  the  plat- 
form, and  also  otf  tiie  platform  on  the  drawing  board,  forming  the 
acute  angle,  as  CGE,  Fig.  2,  Plate  29.  Then  place  the  wreath 
on  its  side,  same  as  above,  with  the  shank  to  agree  with  one  in- 
clination; then  sight  the  other  shank  to  see  if  it  agrees  with  the 
other  inclination;  if  so,  the  wreath  is  correct. 

To  find  the  twist  lines.  Carry  the  minor  axis  on  the 
plumb  across  the  wreath-piece,  as  9  9;  bisect  9  9,  Fig.  9;  center 
9  9  at  13  with  the  gauge  used  at  section  P,  for  the  center 
of  plank;  set  off  half  the  thickness  of  rail  on  each  side  of  13; 
do  the  same  on  the  convex  side  of  wreath.  Now  we  have  three 
points,  11,  14,  12,  through  which  to  bend  a  pliable  strip.  Be 
careful  when  bending  the  strip  to  keep  it  square  with  the  joint  at 
the  shank. 


114  1*I,ATE  24. 

Use  the  try  square  oflen  at  the  shank  joint  when  working  off 
the  over  wood,  applying  the  stock  to  the  Joint  and  the  blade  to 
the  straiglit  part  of  shank  at  times. 

After  the  surplus  wood  is  removed  from  the  top  side  of 
wreath-piece,  then  gauge  for  the  thickness  using  the  Cupper  gauge. 
On  small  wreaths,  the  learner  will  discover  at  the  center  joint,  the 
gauge  will  cut  below  the  block  pattern  at  1.5,  as  shown  by  the 
dotted  line,  while  at  the  opposite  side  the  gauge  will  cut  at  the 
corner  of  block  pattern.  This  arises  partly  from  the  direction  of 
the  joint  on  the  concave  side;  in  small  cylinders  the  joint  is  more 
of  a  plumb  joint  than  a  perfect  butt  joint;  on  the  convex  side  the 
joint  will  be  found  to  be,  or  nearly  so,  a  perfect  butt  joint;  in  large 
cylinders  and  narrow  rails  the  center  joist  is  nearly  a  perfect  butt 
joint  both  on  the  inside  and  also  on  the  outside  of  rail. 

The  learner  must  be  careful  to  allow  plenty  of  over  wood  at 
the  center  joint  until  he  has  the  two  pieces  bolted  together,  then 
dress  down  to  please  the  eye  and  touch,  so  as  to  avoid  all  abrupt 
places. 

Fig.  10.  Shoivs  hoiv  to  place  the  easement  pattern  for  mark- 
ing the  points  to  cut  the  straight  rail. 

Draw  a  tread  [10'''']  and  rise  [7^'']  and  the  level  landing: 
through  the  center  of  short  baluster  XX  draw  the  under  side  of 
rail,  place  the  lower  edge  of  pattern  along  the  line  XX,  and  slide 
up  until  it  will  measure  a  half  rise  [3>^''^J  from  the  floor  line  to 
the  point  A. 

Now  draw  the  face  of  landing  rise  across  the  pattern,  marking 
the  center  at  B  for  the  point  from  which  to  measure  for  the  length 
off  the  platform.  Then  from  Cto  joint  A  equals  \Z]4'^,  to  allow 
for  the  easement  on  the  level. 

At  F  the  length  of  a  regular  long  baluster  is  shown  Z^i'^ 
longer  than  a  regular  short  baluster,  and  at  H  the  baluster  is 
shown  2)4''  longer  than  a  regular  short  one,  and  at  J"  the  baluster 
is  shown  Z%  longer  than  a  regular  short  one. 

Fig.  11.  Exhibits  a  straight  easement  starting  from  a 
neiocl  post. 

Elevate  2  or  more  risers  and  treads;  through  the  center  of 
baluster  XX,  draw  the  under  side  of  rail,  parallel  with  XX  draw 
the  center  line  of  rail  AB;  from  the  top  of  first  steps  set  up  to 
the  under  side  of  rail  the  difference  that  the  newel  is  longer  than 
a  short  baluster,  say  4X'",  and  the  half  thickness  of  rail  [l¥'''l 
more  to  the  center  of  rail  at  O.  From  O,  draw  a  line  parallel  to 
the  first  step  to  intersect  the  inclination  of  the  center  of  rail  at  A; 
plumb  with  No.  1  rise,  draw  the  center  O  of  rap;  from  the  center 
O,  draw  the  verge  of  cap  \Z}4^^],  cutting  OA  at  F.  Make  jPC 
equal  the  half  width  of  rail  [2^'],  then  C  is  the  point  of  miter: 
parallel  with  CA,  draw  the  half  width  of  rail  to  intersect  the 
verge  of  cap  at  D  and  E. 

Through  JE  and  D,  and  at  right  angles  to  CA,  draw  ED 
indefinite,  cuttinar  CA  at  J.  Make  AL  equal  AJ;  from  L  draw 
The  radial  line  LH,  at  right  angles  to  AL,  then  H  is  the  center 
to  draw  the  curves  for  the  easing  pattern.  Prolong  the  face  of 
No,  2  rise  to  intersect  the  center  line  of  rail  at  K,  then  KB  shows 
T}4''  to  joint,  to  be  deducted  when  cutting  the  straight  rail. 

Fig.  12.    Shows  a  square  section  of  rail. 

The  dark  shade  indicates  the  rail-bolt  at  the  center,  a  dowel 
on  each  side  of  the  bolt  keeps  the  rail  from  turning  at  the  joints, 
and  should  be  used  in  all  good  work,  so  that  when  the  joints  are 
dressed  off  they  remain  substantial.    The  hollow  dowel  suits  best 


Plate  24.  115 

at  the  center  Joint,  for  then  the  wreath-piece  can  be  turned 
around  on  the  joints,  the  dowel  keeping  them  from  sliding  off  the 
center. 

Cutting  and  jointing  the  rail  at  the  bench. 

The  first  length  from  spring  of  turnout  to  the  spring  line  of 
cylinder  at  platform  is  11^  8'^  See  Fig.  2,  Plate  22.  Now  we 
have  6'''  of  straight  wood  on  shank  of  face-mould.  Fig.  4,  and  6^^ 
on  shank  of  face  mould.  Fig.  7.  Then  11^  8^^—Q^^-j-Q^'^lO^  8^' 
for  the  measure  to  cut  the  straight  piece  for  the  first  length. 

Again,  the  second  length  from  spring  of  cylinder  at  the  plat- 
form to  the  face  of  rise  landing  equals  2^  11%^^,  and  we  have  to 
allow  6^^  for  shank  at  face-mould.  Fig.  7,  and  ti};^^^  for  straight 
wood  on  lower  end  of  easement,  Fig.  10;  then  2^  11%'''' — 6'^+ 
6X''=i''  IIM^'  for  the  length  to  cut  the  straight  rail  off  the  plat- 
form. The  third  length  from  face  of  landing  rise  to  spring  of 
quarter  cylinder  equals  5^  6>^'^  from  which  deduct  13^4^'''  for  the 
easement  landing.  Fig.  10,  js'  G}.i^^—V  134^^=4^  o}4^q  equals 
V  o}i^^  for  the  length  to  cut  No.  3.  From  the  spring  of  quarter 
cylinder  to  wall  equals  S''  V,  Fig.  1,  Plate  23,  from  which  deduct 
fi"  for  shank  on  quarter  turn,  see  Fig.  5.  [3'  1^'— 6'':==2''  7^^J 
equals  2^  7^^  for  to  cut  the  straight  rail  for  No.  4  length. 

Hanging  Rail.  This  part  of  the  work  every  stair-builder 
has  a  way  of  his  own;  a  very  good  plan  is  to  first  have  the  mor- 
tise for  the  balusters  cleaned  out,  the  brackets  fit  and  nailed  on, 
and  the  nosings  fitted  and  dressed  off.  Now  number  the  nosings 
and  lay  them  aside,  then  mark  the  center  of  baluster  V^  from  the 
end  of  step,  and  2'^  more  to  the  convex  side  of  rail,  [l^^~\-2^^=y^] 
equals  3^^  from  the  end  of  step  or  the  bracket  Hue,  to  the  convex 
or  outside  of  rail. 

Then  mark  a  few  steps  3''''  from  the  ends,  also  around  the 
cylinder  on  the  platform  and  along  the  level,  for  points  to  plumb 
the  rail.  Next  place  the  first  length  of  straight  rail  on  the  nos- 
ings, keeping  the  convex  side  to  the  points  marked  on  the  steps; 
now  try  the  plumb  bob  at  the  end  of  wreath-piece  at  the  platform, 
and  down  the  side  of  rail  when  correct,  plumb  through  the  center 
of  cap  for  the  center  of  newel  post  on  the  floor. 

While  the  rail  is  in  this  position,  measure  from  the  floor  to 
underside  of  cap,  say  that  it  equals  13''^;  then  at  the  center  of  a 
short  baluster  measure  from  the  top  of  step  to  the  under  side  of 
rail,  say  that  it  measures  13  j'''';  then  13^''  minus  1}4'^  equals  IIK^'' 
that  the  newel  post  is  longer  than  a  short  baluster  at  its  center 
when  in  position. 

For  example,  2^.1}4^^,  say  the  height  of  a  short  baluster  when 
in  position  measures  2. 1 3^  at  its  center,  from  the  top  of  step  to  the 
underside  of  rail;  now  the  newel  from  floor  to  under  side  of  cap 
equals  [2'  iy/'-^n}4^^='y  1^^]  three  feet  one  inch. 

Now  set  and  fix  the  newel  to  the  center  on  floor  and  height 
iust  found*  [3''  1^^];  then  hang  the  rail  firmly  on  stanchions; 
glue  and  drive  up  the  nuts  on  the  rail  bolts,  plug  the  holes  made 
for  the  nuts,  see  that  the  rail  is  straight  between  the  crooks,  then 
plumb  and  bore  for  the  balusters;  now  dovetail  and  glue  in  the 
balusters.  Before  glueing  be  careful  to  see  that  the  rail  is  straight, 
without  any  bends.  Often  the  straight  rail  is  bowed,  and  can  be 
straightened  nicely  when  putting  in  the  balusters.  Next  nail  on 
the  nosings.  Trim  down  the  wall  string  and  spandril  under  the 
stairs,  leaving  the  hand  rail  for  the  last  job  to  dress  down,  so  the 
finisher  may  apply  a  coat  of  "filler"  immediately  after  the  stair- 
builder  has  completed  his  work. 

*The  post  may  be  cut  to  length  in  the  shop  and  set  in  place,  and 
the  rail  hung  at  once  in  the  building,  but  the  method  described  above 
is  considered  the  most  economical  iu  the  end. 


Plate  S5 


PLATE  25. 

Plate  25.  [Scale,  H''=l  foot].  Exhibits  the  plan  and 
elevation  of  a  tivo-story  stair  case.  In  the  first  story  the  stair- 
case is  ilivided  into  two  Jlights;  the  first  flight  lands  on  a  lyUitform 
lercl  with  the  floor  in  the  hack  hnildimj,  thc7i  braiiches  ofl,  and 
lands  on  the  floor  in  the  second  story.  And  in  the  second  stonj, 
leading  to  the  attic,  the  stair-case  is  composed  of  one  continiutu-i 
fiiiflit. 

The  height  of  the  first  story  is  11''  1''^  from  top  to  top  of  joist; 
the  height  of  the  first  story  back  equals  9^  4'^;  the  width  of  joist 
in  the  second  story  is  10^';  ilie  width  of  hall  iu  the  rough  is  8^  2^^. 
The  lieight  of  second  story,  from  top  to  top  of  joist,  equals  10'  0"; 
widtli  of  joist  in  third  floor  is  10^';  steps  are  1)4^'  thick;  nosings 
are  to  be  returned  ovei-  lirackets;  size  of  rail  4>^''x2?i''',  fiat 
moulded. 

Now  we  have  11''  V  for  the  height  of  the  first  story,  which, 
reduced  to  inches,  [11^  l'^X12''=i;!3'']  equals  1:53'^  to  be  «li- 
vided  by  ?'',  equals  19,  for  the  number  of  risers  in  tlie  first  story. 
Now  the  height  for  tlie  first  story  back  equals  9'  A^\  which,  re- 
duced to  inches  [9' 4"X12''~112''J  equals  112'^;  that  being  di- 
vided by  1''  [112'''-J-T'''':=16]  equals  16,  for  the  number  of  risers 
to  the  platform.  That  leaves  three  [3]  risers  for  the  short  flight 
landing  in  the  second  story. 

For  the  tread  take  Blondel's  formula,  but  use  for  a  constant 
25'^  for  an  easy  step  [2.5'^— 7''+7'^=ll'']  equals  11^'  for  the 
tread  or  cut  on  horse.  '' 

For  the  flight  in  the  second  story  leading  to  attic  we  have  IC 
C  for  tlie  height,  whicli,  reduced  to  inches,  [10'  0''X12''=^120''] 
equals  120";  that  being  divided  by  8  [120''^  8''=1.5]  equals  15 
risers  to  the  attic;  then  for  the  relative  width  of  tread  to  the 
lieight  of  rise,  by  the  above  formula  and  constant  [2r/' — s^'-j-S''' 
-—W\  we  have  9''  for  the  width  of  tread  by  S''  rise  for  the  cut 
ttut  of  horse. 

Fig.  1.     Shows  Hie  plan  for  the  first  story. 

The  Vv'ell  hole  is  12''  ))elween  the  outer  strings;  the  cylinder 
uiil  then  have  a  radius  of  6".  The  width  of  half  pace  from  the 
luce  of  cylinder  to  wall  should  equal  the  half  width  of  hall  [4'  1"]. 
But  this  cannot  always  be,  for  in  cramped  places  the  room  will  not 
allow  more  than  the  length  of  a  step,  and  should  never  be  less 

Now  in  a  12"  cylinder  with  the  steps  laid  out  on  the  center 
line  of  rail,  there  will  be  about  2"  from  the  face  of  the  landing 
rise  [No.  ItjJ  to  the  face  of  platform  joist,  see  Fig.  1,  Flate  26. 
Then  if  we  allow  4'  0"  from  tlie  wall  to  the  face  of  the  platform, 
and  2"  more  to  face  of  the  landing  rise,  and  1.5  treads  at  11" 
each,  we  will  have  [15Xll'^=lt35"H-12"=l'j'  9"+2"-4'  0"= 
17'  11"]  for  the  run  of  first  flight,  including  the  platform  17'  11" 
as  shown  on  plan,  Fig.  1. 

And  for  the  flight  of[  the  platform  we  have  4'  0"  for  the 
width  of  platform,  and  2"  from  the  face  of  platform  to  face  of  the 
first  rise  off  the  platform,  and  two  treads  at  11"  each;  also  allow 
6"  beyond  the  face  of  last  rise  to  the  face  of  trimming  joist  to 
allow  "the  bearers  a  good  bearing  against  the  joist  for  nailing;  tliis 
then  will  give  us  [2Xll^'-!-2"-^G"-f  4'  0"=6'  6"]  from  the 
wall  to  the  face  of  joint  landing  including  the  platform  C  6".  as 
shown  on  plan. 


Plate  25.  117 

The  next  to  decide  !s  the  distance  out  from  the  back  wall  the 
second  flight  will  come,  as  that  will  determine  the  head  room  for 
tlie  first  flight.  The  cylinder  landing  in  the  third  stor^^  we  will 
keep  plumb  over  the  cylinder  at  the  platform  in  the  flrst  flight; 
Iben  we  will  have  4'  0^'  for  the  width  of  landing,  and  1'^  more 
to  face  of  rise,  then  14  treads  at  K)"  each,  and  %"  more  from  the 
face  of  No.  1  rise  to  the  ronuh  ioist  to  admit  the  cvlinder. 

Therefore  [14X9^'=12«''-^1-'=10'  li^'+4' id"^\"^yi,"~\\' 
1%"\  we  will  have  for  the  whole  distance  from  the  back  wall  to 
the  trimmer  at  the  starting  of  the  flight  in  the  second  story  14' 
">%",  as  f^howu,  Fig.  3. 

Headway  for  the  First  Flight.  The  horizontal  dis- 
tance from  wall  to  face  of  trimmer  in  the  second  story  equals  14'' 
VJg",  from  which  deduct  4'  Q'^  for  platform,  and  2'^  from  plat- 
form to  face  of  No.  16  rise  [14'  1%  "—A'  (i''~^"^W  h% '■']  eqiial.-i 
say  10'  0 '',  which  being  rednecd  to  inches  and  divided  by  the  width 
of  a  tread  [11'']  in  the  flrst  flight  (10'  6"X12"=l:i6"---ll"=--ll 
4"]  gives  eleven  full  treads  and  four  inches  more  to  count  down 
from  the  platform  to  plumb  under  the  face  of  the  trimniing  joist 
in  the  second  story,  which  brings  us  4"  over  on  Xo.  4  .--te)).  This 
then  leaves  the  height  of  four  risers  (28")  at  the  starting  plus 
the  width  of  joist  [10"J  in  the  second  story,  also  the  thickness  of 
floor  [1"].  and  plastering  [1"],  to  be  deducted  from  the  whole 
height  [11'  1"]. 

Then  [2S"-i-10"+l"+l"H-12=.r  4"]  the  height  of  the 
^tory  11'  1"  minus  3'  4"  equals  7'  9"  for  the  headway  as  shown 
Fig.  2,  the  joist  will  round  off  at  D,  and  allow  perhaps  2"  more 
which  will  be  ample  headway,  for  the  first  flight. 

Width  of  Landing  Pace.  For  the  width  of  framing  for 
the  landing  pace,  take  the  Jialf  width  of  hall  [4'  1"],  and  deduct 
[6"J  for  half  the  cylinder,  and  1"  for  thickness  of  front  string, 
[4'  1"— 6"-rl"=3'  6"]  and  we  have  3'  6"  for  the  width  of  land- 
ing pace  in  the  rough,  which  if  deducted  from  the  whole  width  of 
liail  [8'  2"—:'/  %"=\'  S"]  equals  4'  8"  for  the  width  to  trim  the 
well  in  the  rongh. 

Length  of  Landing  Pace.  Now  we  have  14'  7?4"from 
the  wall  to  face  of  trimmer  in  the  second  story,  and  6'  6"  from 
the  wall  to  the  fare  of  joist  at  the  landing,  then  14'  1%"  minus 
'i'  G"  equals  8' 2"  nearly,  for  the  length  of  landing  pace  as  shown. 

The  next  will  be  the  head  room  for  the  tiiyht  in  the  second 
-tory;  the  height  of  rise  is  8",  and  the  tread  9";  we  will  count 
■  iown  1:5  risers  at  8"  each.  [13X8"-^12"— 8'  8''J  that  will  equal 
'  8".  Then  the  depth  of  joist  in  the  third  floor  is  10".  and  the 
plastering  and  flooring  may  be  counted  at  2"  more,  [S'  8" — 
1(7S^2"=::7'  8"]  which  equals  7'  8"  from  the  top  of  No.  2  step  to 
the  ceiling.  We  will  then  place  the  faseia  on  headway  trimmer 
plumb  over  the  center  of  No.  2  step  and  have  very  good  head-room 
tor  the  second  story  flight  going  to  the  attic. 

The  distance  from  back  wall  to  the  face  of  trimmer  at  head- 
way will  be  equal  to  12  treads  at  0"  each,  one-half  tread  4><". 
.ind  4'  0"  from  the  wall  to  the  face  of  trimmer  at  the  landing,  and 
?.''  more  from  the  triunner  to  face  of  No.  ].5  ri^e  and  the  thick- 
ness of  fascia  at  headway,  [12Xa'^-r^K'^-r'l'  0"-r2'^=13'  G^"] 
equals  for  the  whole  distance  13'  ti'^  ".  from  the  wall  to  the  face 
of  trimmer.  Then  13'  6M"— 4'  0"=9'  ^W,  for  the  length  to 
frame  the  well:  and,  as  the  cylinder  in  the  attic  has  the  same 
radius  as  iu  the  first  story,  the  well  will  have  the  same  width  of 


lis  Plate  25. 

opening,  i^  &^^\  then  the  trimming  of  the  well  in  the  attic  will 
be  4^  8^^  by  9'  6^^^  in  the  rough. 

Fig.  1.  At  P  is  shown  the  manner  of  building  the  plat- 
form. The  flooring  will  run  in  the  same  direction  as  the  steps 
wherever  this  can  be  done;  more  satisfaction  will  be  the  result. 
A,  A,  A,  are  the  bearers,  3'''  bj'  4^^  scantling.  They  are  doubled 
at  the  outer  string  on  the  long  flight.  At  JB,  B,  B,  the  dotted 
lines  show  the  rough  brackets,  the  center  bearer  having  two  rows, 
one  on  each  side.  The  center  of  newel  post  is  placed  in  the  cen- 
ter of  hall.  The  arc  and  radius  for  the  turnout  is  determined 
fi'om  the  difference  that  the  newel  post  is  longer  than  a  siiort 
baluster,  and  the  location  of  newel  see  explained  Plate  26.  Fig.    1 

Fig.  2.  Slwws  the  elevation  of  tirst  flight  of  16  rinens 
landing  on  tlie  platform,  ttienee,  icith  3  risers  more,  hranchiiuj 
off  and  landing  in  tlie  second  story. 

SS  shows  the  front  string;  WW  the  wall  string;  J,  J.  J. 
shows  the  joints  of  cylinder  connecting  tl.e  front  string;  AB 
shows  the  story  rod  divided  off  to  the  required  number  of  risers 
[19].  At  C  is  shown  the  pitch-board,  made  to  suit  the  height  of 
rise. 

At  ^Pthe  run  of  treads  is  spaced  off  on  a  rod.  H  shows 
the  pitch-board  made  to  suit  the  tread.  The  correct  lise  and  tread 
should  be  entered  in  the  order  book,  as  the  pitch-board  is  liable  to 
shrink.  At  Q  is  shown  the  panel  work  underneath  the  first  flight 
continued  to  the  joint  of  cylinder,  having  an  arch-way  for  a 
wash-stand  or  coat  closet.  At  K  is  shown  the  rough  bracketing 
underneath  the  steps. 

Fig.  3.  Slioios  elcvaliun  of  the  flight  leading  to  the  attic, 
having  a  utruight  run  of  15  risers. 

MN  shows  the  story  rod  spaced  olf ;  AC  shows  the  run  spaced 
o<T  into  the  required  number  of  treads;  at  O  aud  JR  is  shown  the 
pitch-board  dressed  oft'  neatly  to  the  rise  aud  tread. 

At  Figs.  2  and  3  are  shown  the  lengths  on  the  front  string  to 
rut  the  rail  and  make  the  Joints  at  the  bench,  so  as  to  save  any 
work  in  jointing  the  rail  in  the  building.  The  lengths  for  the 
levels  must  he  taken  in  the  building  after  the  stairs  are  up,  and 
afterwards  entered  in  the  order  book. 

The  first,  or  No.  1  length,  from  joint  of  turnout  to  joint  of 
eylinder  at  the  ])latform,  is  14'  0'4'";  No  2  length,  from  joint  of 
cylinder  to  the  face  of  landing  rise,  is  V  ^H^^\  No.  .3  length  is 
shown  taken  from  the  face  of  landing  rise  to  joint  of  cylinder 
starting  off  the  second  flight,  and  is  8'  Q%''\  No.  4  length,  12' 
S}^'',  is  taken  from  joint  to  joint  of  cylinder;  No.  5  length,  8' 
A^^',  is  shown  taken  from  the  joint  of  cylinder  landing  to  joint 
of  quarter  cylinder;  No.  6  length  is  taken  from  the  joint  of  quarter 
cylinder  to  the  wall,  and  equals  4'  V.  All  lengths  must  be  taken 
parallel  with  the  lower  edge  of  string. 

The  stair-builder  should  take  time  and  figure  out  the  dif- 
ferent dimensions  around  the  well,  on  the  spot,  so  that  the 
carpenter  can  trim  and  lay  the  floors.  By  so  doing  he  will  give 
better  satisfaction  and  be  more  economical  to  himself.  For  this 
reason  the  young  man  should  familiarize  himself  in  figtiring  out 
these  dimensions. 


Plate  26.  119 


PLATE  26. 

Plate  26.  [Scale,  54^^=1  foot].  Exhibits  the  construction 
of  the  cylinders  and  strings;  also,  how  to  find  the  radius  and 
position  of  the  lasers  in  the  turnout  at  newel  for  the  stMr-case. 
Plate  25. 

Fig.  1.  Sfioivs  plan  of  a  platform  cylinder  12^'  in  diame- 
ter, and  hoxo  to  place  the  risers  and  treads  on  the  center  line  of 
rail  equal  to  those  in  the  straight  run  [7^^X-'^^']- 

This  has  been  fully  explained  at  Plates  15  and  16,  and  is  shown 
iK'ie,  together  with  FIl's.  2  and  3.  more  to  illustrate  the  joining  of  the 
.  ylinders  to  the  straight  strings. 

Now,  the  balusters  are  2-"  square,  and  must  stand  flush  with 
the  face  of  bracket,  which  is  K^''  thick.  Then  the  center  of  bal- 
uster will  be  back  from  the  face  of  outer  string  %^^,  and  the 
radius  for  the  center  line  of  rail  will  equal  6H^\  With  6%^''  for 
a  radius  and  O  as  a  center,  draw  the  semi-circle  ABC;  through 
O.  <lraw  CA  prolonjied;  at  right  angles  to  AC,  draw  AK  and 
CS  for  the  direction  of  straight  string. 

With  OB  as  a  radius  and  B  for  a  center,  draw  the  arc  inter- 
secting the  center  line  of  rail  at  2:  through  2  and  B  draw  a  line 
produced,  cutting  CA  at  X  and  SC  prolonged  at  3;  then  C3  is 
the  stretchout  for  half  the  semi-circle. 

Now,  from  3  space  off  half  a  tread  i^M"^  to  face  of  No.  17 
rise;  from  the  face  of  No.  17  rise  set  off  a  regular  tread  (11")  to 
No.  18  rise;  draw  Nos.  15  and  16  risers  opposite  to  Nos.  17  and  18; 
locate  a  short  baluster  on  Nos.  15  and  IS  steps,  and  space  off  the 
balusters  around  the  cylinder.  Then  curve  Nos.  16  and  17  risers 
to  suit  the  balusters. 

At  S  is  shown  the  thickness  of  string  {^\i").  iVJV shows 
the  nosings.  The  faces  of  Nos.  15  and  IS  risers  are  located  ^%" 
from  the  diameter  line  AC, 

Fig.  2.  Shows  the  cylinder  starting  from  the  level  to  rake 
In  the  second  story. 

The  manner  of  finding  the  stretchout  and  placing  the  risers 
is  the  same  as  described  for  Fig.  1,  only  in  this  the  treads  are  9'''. 
Make  from  3  to  face  of  No.  1  rise  equal  half  a  tread  (432''''),  and 
make  from  No.  1  to  No.  2  rise  equal  a  regular  tread  (9''),  thus  lo- 
cating the  face  of  No.  2  rise  2)i^^  from  the  spring  or  diameter  of 
cylinder.  Locate  the  short  baluster  on  No.  2  step  irom  that; 
space  off  the  required  number  of  balusters  around  the  cylinder, 
and  curve  No.  1  rise  to  suit  the  balusters. 

Fig.  3.  Shovjs  tlie  plan  of  cylinder  landijig  on  the  level  n? 
th-e  third  story. 

The  solid  lines  show  the  cylinder  and  the  face  of  rises.  The 
outside  dotted  line  ABC  shows  the  center  line  of  rail  ^^^  out 
from  the  cylinder  line;  C  3  shows  the  stretchout  from  C  to  B. 
From  the  point  3  set  oft'  half  a  tread  (i.W'')  to  face  of  No.  15 
rise,  which  is  drawn  on  the  opposite  side.  From  face  of  No.  15 
to  No.  14  rise  equals  a  regular  tread  (9'^),  making  the  face  of  No. 
14  rise  2X^^  fi'om  the  spring  of  cylinder.  Locate  the  short  bal- 
uster on  No.  14  .tread;  from  that  space  off  around  the  cylinder  or, 
the  center  line  of  rail  the  required  number,  then  curve  No.  15  rise 
to  suit  the  baluster.  A  better  way  to  place  the  risers  in  the  cyl- 
inder for  startings  and  level  landings  is  shown  in  Figs.  1  and  5, 
Plate  16,  where  one  set  of  face  moulds  is  made  to  answer  for  both 
cylinders. 


ISO  Plate  25. 

Pig.  4.  Shows  hoiv  to  determine  the  radius  of  the  turnout 
from  the  height  and  position  of  the  neicel  j)ost. 

We  will  say  the  newel  post  is  G'''  higher  than  a  short  baluster 
from  the  top  of  step  to  the  under  side  of  rail,  at  the  center  of  bal- 
uster. 

Elevate  two  or  three  risers  as  Nos.  1,  2,  3  and  4;  through  the 
center  of  short  baluster  XX  draw  the  under  side  of  rail;  make 
XC  half  the  depth  of  rail  (IM^O;  diaw  CD  parallel  with  XX 
for  the  center  of  rail:  from  the  top  of  No.  1  step  set  up  6'"  to  llui 
under  side  of  rail,  and  l.?s^^  more  for  the  center  of  rail  at  JE, 
draw  ED  parallel  with  top  of  firs-t  step  to  intersect  CD  at  D.  At 
any  convenient  point,  and  parallel  with  J7Z>,  draw  AS  to  indicate 
the  center  line  of  rail.  Now  ^et  the  center  of  newel  O  on  Une 
with  the  face  of  No,  1  rise,  and  Oyi''^  out  from  the  center  line  of 
rail;  from  D  drop  the  perpendicular  to  intersect  AB  at  F.  Join 
OF;  from  tho  center  O  draw  the  verge  of  cap  7^'  in  diameter,  and 
cutting  OJPat  H.  Make  H2  equal  half  the  width  of  rail  (SJ^'O 
also  set  off  on  each  side  of  OJPhalf  the  width  of  rail  to  cut  the  cap 
at  3  and  4;  join  3  4,  intersecting  OF  at  5;  then  make  jPJ" equal 
F  5,     Then  FJ  and  F  5  are  the  It^xsrth  of  tangents  on  the  plan. 

From  J,  and  perpendicular  to  FJ,  draw  JR  indeiiuite;  from 
0.  and  at  right  angles  to  5  F,  draw  5  JFJ,  intersecting  JR  at  R; 
then  il  5  is  the  radius  (2^  2'")  for  the  turnout  at  the  center  of 
rail,  and  %^^  less,  or  2''  1^4^^  is  the  radius  for  the  curve  of  front 
string  6  7;  draw  7  8  parallel  with  AJB. 

Now  carry  down  the  face  of  No.  1.  2,  3  and  4  risers  from  the 
elevation  to  plan.  Nos.  1,  2,  3  and  4  show  their  position  on  plan. 
The  face  of  No.  3  riser  is  shown  on  plan  4>^^^  out  from  the  joint 
of  the  turnout;  the  radius  and  position  of  risers  for  the  turnout 
are  now  shown  as  required  for  prejjariug  the  turnout,  steps  and 
risers  for  the  same. 

This  drawing  should  he  luado  on  paper,  then  after  tlie  steps  are 
prepared,  the  drawing  can  be  rolled  up  until  the  rail  is  required. 

Fig.  5.  Shows  the  semi-circle  divided  off  into  an  odd  num- 
ber (5)  of  staves. 

Then  the  back  surface  of  the  center  stave  will  lay  solid 
against  the  face  of  platform.  AJ3  shows  the  edge  of  drawing 
board;  CD  is  a  gauge-line  run  on  for  the  diameter  of  cylinder. 
From  0  draw  the  semi-circle  to  a  radius  of  6^^;  space  off  the  semi- 
circle into  the  required  number  of  staves,  as  D  2,  2  3;  join  2  D 
prolonged  to  edge  of  board  at  M  for  a  handy  means  to  set  the 
bevel  from  the  edge  of  board  as  shown.  SS  shows  the  edge  of 
face  string  and  manner  of  connecting  the  cylinder  by  splicing  and 
drawing  the  joint  up  with  screws  from  the  back. 

Fig.  6.    Shows  the  quarter  circle  divided  into  two  staves. 

The  face  of  one  stave  is  prolonged  to  cut  the  edge  of  draw- 
ing-board to  set  the  bevel  as  shown. 

Fig.  7.  Shows  the  wpiycr  and  lower  ends  of  wall  string  for 
the  first  flight,  and  is  laid  off  as  has  been  described  at  Fig.  2, 
Plate  19. 

AB  is  the  gaug«  e,  run  on  10%'''  from  the  upper  edge; 
one  inch  is  allowed  for  e  grounds,  which  is  worked  on  the  solid 
as  shown  at  C;  the  compasses  are  set  to  the  hypothenuse  of 
pitchboard,  and  the  required  numb  r  of  risers  are  spaced  off  on 
the  gauge  line  as  00;  DD  shows  the  wedge's;  the  wedge  for 
riser  being  entered  first  and  those  for  the  step  last. 

At  EE  the  string  is  gained  half  through  to  join  with  the 
base;  FF  shows  the  base  moulding,  it  is  rebated  on  the  lower 
edge  to  drop  down  on  the  base  H^^  as  shown  at  C 


Plate  26,  121 

Pig.  8.  Shows  t?e  vpper  and  loiver  ends  of  the  front  or 
outer  strUig. 

AB  shows  a  gauge  line  run  on  lightly  as  a  guide  for  the 
pitchboard  as  showu  at  P,  Fig.  10;  the  points  O,  O,  0,  &c.,  along 
the  lower  edge  are  transferred  from  O,  0,  O,  &c.,  on  the  wall 
string.  Fig.  7,  then  squared  over  to  intersect  the  gauge  line  AB 
at  XXX,  Ac. ;  if  the  pitchboard  is  applied  to  these  points  care- 
fully, the  two  strings  cannot  fail  to  be  both  of  the  same  length. 

Cylinder  Joints.  At  Fig.  l  the  face  of  No.  15  rise  is 
showu  5%^'  from  the  joint  of  cj  Under.  Now  as  the  end  of  rise  is 
reduced  to  H^^  thick  for  to  miter  with  the  brackets,  the  distance 
from  the  cut  out  of  string  to  joint  of  cylinder  will  be  H^^  less, 
making  5^'^  as  shown;  the  joint  CD  is  10%'^  long.  Then  the 
joint  of  turnout  at  Fig.  4  is  shown  from  the  face  of  No.  3  rise  to 
joint  4>^^^  in  this  case,  the  }i'^  will  be  added,  making  4^^'  from 
the  cut  out  of  No.  8  rise  to  the  spring  FE  of  turnout. 

No,  1  rise  is  shown  reduced  to  5^4",  allowing  the  thickness 
of  a  step  1H'\  that  when  the  step  is  in  place,  the  risers  will  all 
be  uniform  in  height.  The  points  from  which  to  take  the  length, 
to  cut  the  rail  are  showu  from  joint  to  joint  of  cylinders,  [14'' 
OH'']. 

Fig.  9.  Shows  f}i€  outer  stHng  having  three  risers  landing 
in  the  second  story. 

The  wall  string  is  not  showu,  but  the  points  O,  O,  on  the 
lower  edge  of  string  are  transferred  from  corresponding  ]!oints  on 
the  wall  string  as  above;  the  points  are  squared  over  to  Intersect 
the  gauge  line,  from  which  to  apply  the  pitchboard. 

At  Fig.  1  the  face  of  No.  18  rise  is  shown  5Ji^^  from  the  joint 
of  cylinder,  then  H^^  more  for  the  reduced  thickness  of  rise  will 
equal  63^^''  from  the  joint  of  cylinder  AB  to  the  cut  out  of  the 
face  string  as  shown.  The  joint  is  11>4^''  long.  At  Cthe  string 
is  notched  K^'  for  the  difference  between  the  thickness  of  step 
{l}4'')  and  the  flooring  (1")  in  the  second  story. 

For  the  full  easement  landing  allow  10'^  for  the  width  of 
joist,  and  X^^  more  for  the  lath  and  plaster  equals  lOX^'-  Then 
draw  FG  parallel  with  CD,  and  ease  off  the  angle  OFG  with  the 
easement  pattern.  HH  shows  two  balusters  on  the  level.  At 
No.  19  rise  the  landing  step  and  rise  are  shown  returned  over  the 
bracket.  The  lengths  to  joint  the  rail  are  shown,  V  ^14"  for  th^ 
short  string  and  8''  0%'^  for  the  level  length,  which  is  taken  from 
the  face  of  No.  19  rise  to  joint  of  cylinder  starling  second  flight. 

Fig.  10.  Shows  the  vpper  and  lower  end  of  the  wall  string 
in  the  second  story. 

The  lining  off  is  the  same  as  has  been  described  for  Fig.  7. 
The  lower  end  is  shown  lined  off  to  the  pitch-board,  and  after- 
wards with  the  housing  pattern.  At  the  upper  end  the  pitch- 
board  Pis  shown  applied  along  the  gauge-line  and  ready  to  apply 
the  housing  pattern.  The  upper  end  is  notched  out  to  fit  up 
against  the  joist  at  the  lauding.  At  A  is  shown  a  triangular  piece 
glued  on  to  form  the  easement.  The  string  is  shown  rebated  on 
the  upper  edge  forming  the  grounds. 

Fig.  11.  Shows  the  upper  and  lower  ends  of  the  outer 
string. 

It  is  lined  out  from  the  wall  string  in  the  same  manner  as 
Fig.  8.  The  joint  AB  is  showu  on  plan  Fig.  2  to  be  2^'''  from 
the  face  of  No.  2  rise.  The  rise  is  shouldered,  allowing  ^4^^  to 
connect  the  bracket.  Then  from  the  joint  to  cut-out  for  No.  3 
rise  will  equal  3>8  ^''.  The  joint  is  10^'"'  long  and  parallel  to  the 
risers. 


123  Plate  27. 

At  the  upper  end  the  face  of  No.  14  rise  is  shown  on  plan 
Fig.  3  to  be  2X^^  from  the  joint  of  cylinder.  In  this  case  the  ^," 
for  rise  must  be  taken  off,  leaving  from  the  cut-out  of  No.  14  rise 
to  the  joint  CD  equal  to  2^^^  as  shown.  Make  the  joints  per- 
pendicular to  the  treads;  the  length  of  joint  equals  \i%" .  The 
length,  12'  %%''■,  for  jointing  tlie  straight  rail  is  taken  from  joint 
to  joint  of  cylinders,  and  parallel  to  the  lower  edge  of  string.  The 
first  level  length  iu  the  attic  (8''  ^M")  is  taken  from  joint  of  cyl- 
inder landing  to  joint  of  quarter  cylinder;  and,  again,  from  joint 
of  quarter  cylinder  to  wall  (4'  1'^)  for  the  last  length. 


PLATE  27. 

Plate  27.  [Scale  Yx^'—X  foot].  Exhibits  a  method  how  to 
obtain  the  length  of  staves  for  the  cylinders  at  Plate  26. 

Fig*  1.  Shows  tlw  development  of  staves  for  the  cylinder, 
Fig.  1,  Plate  26. 

Let  AB  indicate  the  edge  of  drawing  board;  draw  Nos.  15. 
16,  17  and  18  risers  and  treads  7^'Xll'^.  Make  CD  equal  6}i^^ 
perpendicular  to  AC  draw  DF;  then  with  the  breadth  of  a  stave 
as  D  2,  Fig,  5,  Plate  26,  space  off  five  staves  and  draw  them  par- 
allel to  DF;  make  LO  [lO^^^J  equal  DC,  Fig.  8,  Plate  26-  also 
makeX>J'(llJ^^O  equal  AB,  Fig.  9.  Plate  26,  join  OF  for  the 
length  of  staves  as  shown.  Observe  the  staves  extend  beyond  the 
steps  at  the  upper  ends  and  also  below  the  inclination  OF  at  the 
lower  end  for  over  wood.  MN  and  CP  show  the  width  of  string 
(6''')  at  the  internal  angle  of  step  and  rise. 

Fig.  2.  Shears  the  dci'clopmcnt  of  sta^'cs  from  the  concave 
side  of  cylinder,  Fig.  2,  Plate  26,  starting  from  the  level  to  rake. 

Let  AB  indicate  the  edge  of  drawing  board;  from  AB  draw 
Nos.  1  and  2  treads  and  risers;  also  line  off  joist;  No.  1  rise  is  re- 
duced }i^^  for  the  difference  in  thickness  of  the  steps  and  fiooring 
boards.  From  the  cut  out  of  No.  2  rise  at  C,  make  CD  equal 
o}^^^  as  shown  at  Fig.  11,  Plate  26. 

Draw  ZJii*  perpendicular  to  No.  1  step;  from  F  space  off  five 
staves  equal  to  D  2,  Fig.  5,  Plate  26,  draw  the  staves  parallel  to 
DF;  from  C,  set  off  6^'  to  lower  edge  of  string  FG,  which  is 
parallel  to  AB;  the  joist  is  10'''',  and  lath  and  plastering  is  X'^- 
Then  drop  down  from  the  joist  10J<^'  to  K;  draw  ifif  jiarallel  to 
the  joist  line,  cutting  G^  prolonged,  at  H^  for  the  lengtli  of  staves 
as  shown;  the  staves  are  shown  to  be  cut  longer  to  allow  for 
trimming. 

Pig.  3.  Shoivs  the  development  and  length  of  staves  for 
Fig.  3,  Plate  26,  landing  on  the  Itrcl  in  tlic  third  story. 

Let  AB  indicate  the  edge  of  drawing-board.  Draw  Nos.  14 
and  15  treads  and  risers;  draw  BC  for  line  of  joist.  As  the  steps 
are  U^'  thicker  than  the  flooring.  No.  15  rise  is  drawn  a  U^^ 
higher.  The  cylinder  is  notched  out,  as  shown,  to  receive  tho 
step.  From  the  face  of  No.  14  rise  set  off  2%^^  to  D.  Draw  DF 
perpendicular  to  No.  14  tread;  from  D^  space  off  five  staves,  each 
equal  to  jD  2,  Fig.  5,  Plate  20.  Make  DF  {Vi}^'')  equal  DC, 
Fig.  11,  Plate  26.  Make  CiT  equal  tlie  width  of  joist  (10''''),  phis 
the  thiokness  of  lath  and  plaster  (X^O-  equals  10%^^  Draw  KH 
parallel  to  the  joist  line  BC;  also,  draw  FH  parallel  to  AB  for 
the  length  of  staves  as  shown.  Cut  the  staves  long  enough  to  al- 
low for  trimming. 


Plaxe  27.  123 

Fig.  4.  Shows  the  sUives  for  Fvj.  1  jnintcd  and  glued  ■up, 
formiiKj  the  cylinder,  ready  to  trim  off  and  i^plice  to  the  strings. 

At  A  and  JB  the  strings  are  shown  gained  in  to  receive  the 
joints  C  and  D  of  ej  Under.  Tlie  joint  at  C  is  10%''^  Jong,  and 
the  joint  at  JD  is  llj^^^  long.  Tlic  twist  line  6,  5,  4,  3,  2,  1,  is 
obtained  by  bending  a  pliable  strip  in  tlie  cylinder  from  1  to  6, 
governing  its  direction  at  the  joints  with  the  pitch-board  by  the 
use  of  a  tack  at  points  1,  6,  4,  5  and  '2;  tiien  by  shifting  the  tacks 
at  5  and  2  the  direction  of  strip  at  the  joints  is  easily  adjusted  to 
the  inclination  of  pitch-board. 

The  jointing  and  preparing  of  the  staves  for  glueing  is  ex- 
plained for  Plate  22.  ( .- 

Fig.  5.  Shows  the  cylinder,  for  the  starling  from  the  level 
to  the  rake,  for  the  flight  in  the  second  story,  and  repeats  Fig.  4 
only  in  this  case:  A  full  easing  is  required  to  connect  the  level 
with  the  rake.  The  width  of  face  string  along  the  level  is  10^-' 
for  the  joist  and  K'^  for  the  lath  and  plaster;  equals  lOX'^.  Then 
the  length  of  joint  at  D  will  be  lOX^';  the  length  of  joint  at  C  is 
shown  lO?!^^  At  A  and  B  are  shown  the  splice  johits  on  the 
ends  of  straight  strings  to  receive  the  joints  of  cylinder  sliown  at 
D  and  C,  which  are  to  be  glued  and  screwed  from  the  back  of 
strings.  The  twist  line  is  found  as  described  at  Fig.  4.  Only 
the  direction  of  strip  at  joint  D  is  regnlated  by  tlie  square  and  at 
joint  C  the  pitch-board  g^^■es  the  direction  of  the  twist  line  to 
agree  with  the  straight  string.  At  the  intermediate  points  5,  4, 
3,  2,  the  learner  mnst  use  his  judgment  as  to  the  direction  so  as 
to  avoid  any  abruptness  in  the  curve.  Also  the  learner  will  dis- 
cover from  experience  that  if  the  direction  of  twist  lines  at  the 
joints  be  a  little  steeper  than  the  pitch-board  it  will  ini])rove  the 
curve  at  the  joints.  The  steps  arc  1}^^^  thick  and  the  tlo<n-  in  the 
second  story  is  one  inch  thick.  For  this  reason  observe  that  No. 
1  rise  is  7^4^''  high  and  the  regular  rise  is  8''^.  This  allows  the 
level  part  of  cylinder  to  come  close  up  under  the  flooring. 

Fig.  6.  Sliows  the  cylinder  for  the  rake  to  level  landing  in 
the  third  story. 

For  laying  out  the  treads  and  risers  in  the  cylinder  use  a  flex- 
ible square  made  from  card  board.  Tiie  joint  at  D  is  lOK''''  long 
and  the  joint  at  C  VoH'^  long.  Always  lay  olf  the  treads  and 
risers  in  the  cylinder  to  agree  with  the  plan  fust,  then  measure 
down  from  the  tread  liue  for  the  length  of  joints.  The  twist  line 
is  obtained  in  Die  same  manner  as  the  preceding.  As  the  steps 
are  a  l^^^  thicker  tlian  the  flooring  Ko.  1.5  rise  is  first  luarked  a 
^\'^  higher,  (lien  afterward  notched  out  to  admit  the  landing  step; 
tiien  the  level  fascia  and  tiiat  part  of  the  cylinder  not  notched  out 
will  come  close  up  under  the  flooring. 

The  lengths  for  jointing  the  straight  rail  to  the  wreath-pieces 
are  shown  taken  from  joint  to  joint  of  cylinders,  and  should  be 
entered  in  the  order  book;  tliose  on  the  level  are  taken  after  the 
stairs  have  been  stepped  uji.  However,  if  the  trimming  of  the 
well  is  all  right,  tiie  level  string  connecting  the  easement  at  the 
laiuling  of  the  lirst  flight,  also  the  level  fascia  in  the  third  story  at 
the  (luarler  cylinder,  may  have  all  their  joints  made  at  the  bench, 
glued  and  screwed  up  in  sections  ready  to  set  in  place  in  the 
building. 

Fig.  7.  Shows  plan  of  turnnut  to  accompany  Fig.  4, 
PkUe  2r,. 

One  plan  will  be  all  that  is  required,  but  to  make  it  plainer  to 
the  learner,  it  is  best  to  divide  it  into  two  or  more  plans;  the  solid 


124  Plate  27. 

lines  show  the  face  of  string;  /S/S  shows  the  thickness  (IK'''')  of 
string;  N  shows  tlie  nosings. 

The  position  of  risers  to  the  radius  and  curve  of  turnout  is 
shown  at  Fig.  4,  Plate  26.  B  is  the  newel  post,  O  the  center 
from  whieli  the  segment  of  cylinder  is  drawn,  it  is  shown  divided 
into  two  staves;  the  bevel  for  the  staves  is  shown  at  C.  The  face 
of  No.  3  rise  is  4}^^  out  from  the  spring  of  cylinder;  the  baluster 
(3^''X2^'')  at  A  is  shown  to  line  on  two  faces  with  the  face  of  rise 
and  bracket,  then  the  center  of  rail  will  be  ?,i'^  from  the  face  of 
string. 

Fig.  8.  Sfiows  the  elevation  of  Xos.  1,  2,  3  and  4  risers, 
anil  the  hjircr  end  of  front  string. 

The  newel  post  is  shown  having  a  tenon  A  through  the  door, 
with  two  pair  of  folding  keys  made  to  press  against  a  piece  of 
timber.  S.  that  is  cut  between  the  joist  and  mortised  out  to  slip 
over  the  tenon  A,  so  that  when  the  keys  are  driven  home  the  post 
will  have  a  linn  foundation.  The  cut  out  of  front  string  is  shown 
4%'^  from  the  joint  of  turnout  CD.  No.  1  step  shows  the  man- 
ner of  constructing  the  step  and  riser.  At  No.  3  and  4  rise  the 
brackets  HH,  and  nosings  JJ",  are  shown  returned  over  the  brackets 
on  the  froiit  string.  The  best  way  to  fasten  the  balusters  in  the 
steps  is  to  dove-tail,  glue  and  nail  them,  if  the  material  is  dry  and 
No.  1  glue  is  used,  the  work  will  remain  substantial;  F  aud  G 
shows  the  base  of  a  short  and  long  baluster  in  position.  Observe 
they  are  cut  a  little  short  of  the  thickness  of  step,  so  they  will  not 
bind  on  the  cut  out  of  string,  but  will  draw  down  close  at  the 
shoulders. 

Fig.  9.  Shows  the  mouhliiKj  on  the  lower  edge  of  front 
^tri}i(].     (vScale  >2  full  size.) 

Fig.   10.     Shoios  the  upper  edije  of  icall  string. 

S  shows  the  string,  G  the  grounds,  P  the  plaster,  B  tlie  base 
moulding,  0  the  rebate  of  base,  H  the  housing  for  step.  The 
grounds  to  receive  the  plaster  is  sliown  worked  on  the  solid;  this 
strhig  is  usually  !}.<''  thick,  and  the  steps  are  housed  in  %^' deep; 
on  brick  walls  allow  %^^  for  plaster,*  and  on  partions  X^^  for  lath 
and  plaster. 

Preparing  the  steps  are  the  .saine  as  has  been  described  in 
Plate  '22  tor  a  T"  cylinder.  This  being  a  vy^  cylinder,  there  will 
be  more  circular  end  steps.  I'atterns  may  be  made  the  same  as 
shown  for  a  7^^  cjlinder,  or  they  may  be  laid  off  from  the  draw- 
ing. If  the  drawing  be  made  on  thick  paper  the  cuiTes  may  be 
pricked  through  on  to  the  stuff  and  afterward  traced  and  dressed 
to  the  required  shape.  For  the  construction  of  the  concave  and 
convex  risers,  see  Fig.  5  and  0,  Plate  31. 

*If  adamantine  or  Keen's  cement  be  used  for  the  -walls,  then  allow 
%"  for  brick  and  ^i"  for  lath  and  plaster. 


Plate  38.  126 


PLATE  28. 

Plate  28.  [Scale  %=:1^J.  Exhlhits  the  manner  of  veneer- 
imi  the  cylinder.  Ttie  true  pitch  of  stairs  is  laid  off  on  the  cyl- 
inder line  instead  of  o^i  the  center  line  of  rail,  as  at  Fig.  1,  Plate 

Fig.  1.  Shows  the  semi-circle  12''  in  diameter  and  the 
stretchout  C  3,  for  the  quarter  circle  is  drawn  in  the  same  way  as 
at  Fig.  1,  Plate  26. 

On  the  stretchout  3  Cset  off  half  a  tread  (5H^^)  to  4,  or  the 
face  of  Xo.  17  rise;  from  the  face  of  No.  17  rise  to  the  face  of 
No.  18  will  equal  a  tread  or  11^',  draw  No.  15  and  16  rise  oppo- 
site to  No.  18  and  17  rise  ;  now  locate  the  short  baluster  on  No. 
15  and  18  treads,  then  space  off  the  intervening  baluster  equal 
and  curve  No.  IG  and  17  rise  to  suit  the  baluster.  The  face  of 
No,  15  and  18  rise  is  shown  1"  from  the  spring  of  cjiinder. 

Fig.  2.    SJimvs  the  thiclincss  of  veneer. 

The  shaded  part  shows  the  staves.  The  string  AA  is 
!}{''  thick  and  is  shown  reduced  at  the  circular  part  sufflcientlj 
to  bend  around  the  drum,  the  reduced  part  is  extended  beyond  the 
spring  line  from  V  to  2'^,  so  as  to  relieve  the  spring  at  the  junc- 
tion of  the  straight  with  the  circular  part  and  thus  avoid  a  possible 
fracture.  To  avoid  making  the  recess  on  the  back  of  string  a 
better  waj-  is  to  make  the  veneer  of  an  even  thickness  throughout, 
then  after  the  veneer  is  lapped  over  the  drum,  lag  out  for  the  full 
thickness  of  string,  thus  avoid  a  tediotis  job  in  reducing  the  string 
to  the  required  thickness. 

How  to  Determine  the  Thickness  of  Veneer : 

Barlow  in  his  experiments  on  the  curvature  of  different  woods 
has  formulated  a  rule  for  the  safe  elastic  limit  before  fracture  for 
three  kinds  of  wood,  oak.  th-  and  larch. 

Rule.  Multiply  the  radius  in  feet  or  a  decimal  of  a  foot  by 
the  constant  for  the  kind  of  wood  used  and  the  result  will  be  the 
thickness  in  inches,  or  the  decimal  of  an  inch.  Thus  the  form^ 
ula  reads; 

For  Oak— the  radius  in  feet  X  0.05=thickness  in  inches. 
"  Fir— the  radius  in  feet  X  0.035=thickness  in  inches. 
"    Larch— the  radius  in  feet  X  0.077=thickness  in  inches. 

For  Example,  suppose  the  radius  of  curve  to  be  33^',  which  is 
equal  to  2'  V.  or  the  inches  reduced  to  the  decimal  of  a  foot 
(9'^-^12=r.75)  would  equal  2.75^ 

Now  3.73^X0.05  for  oak  equals  .1375  of  inch.  This  reduceil 
to  sixteenths  (.1375X16=3.3000)  equals  3.200.  or  say  two-six- 
teenths strong. 

For  white  pine  the  constant  0.0625  will  be  about  right  and 
would  not  injure  the  elasticity  of  the  wood.  Of  coiu-se  straight 
grained  lumber  should  be  selected  for  veneering  in  all  cases. 
Suppose  then  we  use  the  decimal  0.0625  for  white  pine  and  the 
radius  of  curvature  is  6^',  or  the  decimal  of  a  foot  equals  .5.  Then 
0,0625X. 5=0. 03125  of  an  inch.  Now  the  decimal  0.03125  reduced 
to  thirty  seconds  (.03125X.32=1. 00000)  equals  one-thirty-second 
(3*2)  of  an  inch  for  the  thickness  of  pine  veneer,  and  for  every 
additional  6''  that  the  radius  increases  the  thickness  of  veneer  will 
increase  one-thirty-second  of  an  inch. 

By  steaming  the  veneer,  this  thickness  may  be  increased  Ijy  2,  but 
in  steaming  hard  wood,  the  grain  becomes  discolored  and  Is  not  to  be 
recommended  for  fine  work  unless  the  wood  be  pine  and  then  painted; 
or  of  walnut  the  discoloring  does  not  show  so  much  when  varnished. 


156    :  Plate  58. 

Fig.  3.     Shoios  the  Vcnccr. 

Tlie  treads  and  risers  shoulil  be  lined  off  with  load  pencil  and 
not  cut  out  until  removed  from  the  drum.  Alter  the  treads  and 
risers  Nos.  14,  15,  16, 17,  18  and  19  are  lined  off,  make  from  the 
cut  out  of  No.  IS  rise  to  ?pring  of  cylinder  equal  734  ^^;  and  from 
the  cut  out  of  No.  15  rise  to  spring  of  cylinder  6%''^;  draw  AB 
and  CD,  each  perpendicular  to  the  treads  for  the  spring  lines  of 
cylinder;  the  points  from  which  to  take  the  lengths  for  jointing 
the  rail  at  the  bench  are  showti  taken  from  the  spring  of  cylinder 
and  parallel  witli  the  lower  edge  of  string. 

The  length  off  the  platform  is  1^.  10>^^^  and  the  level  length 
is  8''  OX''''  to  the  joint  of  cylinder;  at  F  the  string  is  notched 
M^^  to  fit  up  close  to  the  floor  at  the  l)ack  of  landing  step;  at  H 
the  string  is  gained  in  for  joining  the  level  fascia;  at  K  is  shown 
a  splice  joint  connecting  the  straight  string. 

Pig.  4.  Shoics  irhat  is  termed  a  drum,  made  to  the  size  of 
well  hole  in  diameter,  having  straight  sides;  AB  indicates  the 
spring  line. 

Fig.  5.  Shrms  the  string  with  the  veneered  part  bent  over 
the  form;  fasten  the  straight  part  at  one  end  firmly  to  the  side  of 
drum  with  two  hand  screws,  keeping  the  spring  line  AB  on  the 
string,  over  the  spring  line  AB  on  the  drum,  if  the  spring  line  on 
the  string  agrees  with  the  spring  line  on  the  drum  at  the  opposite 
side,  then  clamp  the  string  down  firmly,  pressing  the  veneered 
part  down  close  to  the  "form."  As  a  precaution  on  small  cylinders 
when  bending  the  veneer  over  the  drum,  put  a  few  staves  across 
tlie  veneer  with  a  screw  at  each  end  temporarily  every  few  inches 
apart,  this  may  save  a  fracture  of  the  veneer;  DD  shows  staves 
cut  out  a  little  longer  than  required,  when  putting  them  oil  com- 
mence at  one  end  and  fit  one  down,  put  a  screw  at  each  end  into 
the  drum,  thus  drawuig  them  closely  to  the  veneer;  then  fit,  glue 
and  screw  the  next,  finishing  up  at  the  other  end.  After  the 
glue  is  dry,  dress  off  the  high  places  on  the  back  of  staves,  then 
tack  and  glue  on  two  courses  of  hard  wood  strips  3^^^  thick  and 
2^^  wide,  in  two  thicknesses.  Let  the  lower  course  be  1^^  above 
the  lower  edge  of  string,  and  the  other  course  far  enough  down 
from  the  upper  edge  not  to  interfere  with  the  cut  out  of  string. 

After  the  glue  is  dry  remove  the  string  from  the  form,  and 
dress  off  the  over  wood  to  the  edge  of  veneer.  If  there  are  mould- 
ings to  be  worked  on  the  lower  edge  of  string,  the  staves  can  be 
extended  and  rebated  to  form  grounds  for  the  mouldings. 

The  woll-liole  finished  in  this  way  makes  flrst-class  work,  and  in 
liard  wood  finish  sliould  always  be  done;  for  tlie  character  of  finish 
in  a  liousc  is  often  deteruiined  by  tlie  appearance  and  workmanship 
of  the  stairs,  thus  adding  to  or  diminishing  the  value  of  the  building. 

Fig.  6.  Shows  (I  method  of  curvin<j  the  front  string  at  the 
turnout,  shoivn  at  Fig.  7,  Plate  27. 

There  the  curve  is  shown  built  with  two  staves,  but  for  hard 
wood  that  is  varnished  the  grain  in  the  straight  part  of  fx"ont 
string  should  continue,  if  possible,  to  include  the  cylinder  as 
shown. 

The  radius  of  the  curve  is  2''  IH^^,  and  the  string  B  can  be 
easily  bent  over  the  form  A  by  cutting  grooves  as  shown  at  1,  2, 
3,  perpendicular  to  the  treads  with  a  cutting  thrus;  or  having 
steam  power,  the  grooves  can  be  cut  in  a  few  miiiutes  witii  the 
circular  saw  over  the  saw  table,  and  all  the  same  depth,  as  that  is 
very  important  to  avoid  kinks  and  have  the  curve  regular. 

After  the  grooves  are  cut,  bend  the  string  over  the  form 
keeping  the  spring  line  on  the  string  over  the  spring  line  on  the 


I'LATK  28.  127 

form,  and  fasten  down  with  hand  screws;  size  the  grooves  with 
thin  glue,  let  drj-,  then  make  keys  of  hard  wood,  and  fit  them  into 
the  grooves  neatly,  so  that  when  glued  and  gently  driven  home, 
they  will  not  spring  the  curve  at  one  place  more  than  at  another, 
and  when  taken  off  the  form  the  curve  will  be  regular,  having  no 
kinks. 

At  B,  it  will  be  observed  that  one  key  is  placed  Ijeyond  the 
spring  line  to  relieve  the  curve  at  that  point.  When  the  glue  is 
dry,  dress  off  the  keys  to  the  curve;  then  glue  and  tack  on  thin 
strips  as  above,  extending  them  over  on  the  straight  part  binding 
the  whole;  the  treads  and  risers  in  the  curved  part  must  not  be 
cut  out  until  the  bending  is  complete. 

The  space  to  allow  from  center  to  center  of  grooves  or  dadoes 
is  3"^^^  for  every  inch  of  radius,  plus  the  width  of  groove,  may  be 
taken  as  a  rule. 

Example,  suppose  the  radius  of  curve  to  be  13'''',  which  equals 
II  plus  the  width  of  groove  i}i''),  equals  (5%''^+3'4— Ig)  for  each 
space  %'^,  to  space  off  the  grooves  for  a  cylinder  2'1'^  diameter. 

In  this  case  the  radius  equals  2534^^  which  equals  |f,  plus 
the  width  of  groove  }i'\  equals  one  inch  (1'^)  for  each  space, 
nearly. 

At  J*  is  shown  the  manner  of  splicing  and  screwing  the  joint 
from  the  back,  the  splice  joint  should  be  near  the  spring  of  cylin- 
der at  the  platform,  where  it  would  not  be  so  noticeable,  for  it  is 
very  difficult  to  make  a  joint  of  this  kind  in  hard  wood  that  will 
not  show  more  or  less. 

Pig.  7.  At  A  is  shown  a  method  of  grooving  the  stops  to 
receive  the  full  thickness  of  rise,  and  the  scotia  F,  is  glued  and 
nailed  in  the  angle  under  the  nosing  H. 

Another  method  is  shown  at  B.  The  step  is  grooved  to 
receive  both  the  scotia  and  rise,  and  at  the  internal  angle  K,  the 
step  is  made  to  extend  to  the  back  of  rise,  and  the  rise  is  side- 
tongued  down  into  the  step.  At  C  the  rise  is  allowed  to  extend 
down  to  the  underside  of  step,  and  the  step  is  side-tongued  into 
the  rise.  The  method  shown  at  K  allows  the  stepping  up  to  begin 
at  the  bottom. 

At  DD  blocks  are  shown  glued  in  the  internal  angle  to  give 
strength  and  prevent  squeaking. 

For  description  of  Figs.  8,  9  and  10,  see  at  the  end  of  letter 
press  for  Plate  39. 

Steps.  The  cylinder,  front  and  back  strings  have  been  lined 
off.  The  next  will  be  to  cut  out  the  steps  and  risers.  The  steps 
are  to  be  1)4^'  thick;  that  will  take  plank  l}i'^  thick,  and  the 
risers  are  specified  %^^  thick. 

Now  take  a  rod  and  measure  off  from  left  to  right  the  half 
width  of  hall  (4^  1^0-  then  to  the  left  half  the  width  of  well- 
hole  (6''^);  then  to  the  right  for  the  thickness  of  bracket,  H^'  and 
\H^'  more  for  the  projection  of  nosing.  This  will  (4''  V — 6"= 
3^7^0+1J4''+M^'=3'8K^O  equals  3' 8>i^^  for  length  of  the 
regular  steps. 

Step  No,  1,  is  .5^''  longer,  No.  2  is  !)<<'''' longer,  and  No.  17  is 
'1)4'^  longer  than  the  regular  length  above.  The  platform  step 
may  be  8^  2'''  long  to  extend  the  full  length  of  platfonn.  In  the 
llight  to  attic  No.  1  step  is  3K'''  longer  than  the  regular  length 
and  the  landing  step  may  be  long  enough  to  include  the  diameter 
of  cylinder  and  2^^  more  to  bed  on  the  joist,  or  13^^  longer  than  a 
regular  straight  step. 

The  risers  may  be  cut  the  thickness  of  step  less  or  3''  7K^'' 
long.     These  lengths  are  taken  between  the  walls,  the  steps  on 


128  Pt-ate  28. 

that  accoiLit  will  be  long  enough  for  fitting  into  the  housings. 
However,  when  taking  the  dimensions  preparatory  to  getting  out 
the  stairs,  see  that  the  walls  are  plumb,  and  note  the  ' '  set  offs" 
of  brick  work,  if  anj%  at  the  height  of  the  different  s'^orys. 

Width  of  S'^'OpS.  The  tread  or  cut  out  c-^  front  string  is 
11^^  the  projection  o';  "osing  is  usually  equal  to  the  thickness  of 
steps  in  this  case  IJ^'''.  The  tongue  at  the  back  of  step  is  ^^^ 
then  the  width  [ll'^+l  H^^+  %"=Vi.%"\  of  steps  equals  \%%^'  for 
the  first  story.  And  the  steps  in  the  second  story  will  equal  ^" 
for  the  tread,  plus  1%  for  the  projection  of  nosing,  and  %^^inore 
for  the  tongue  at  the  back  of  step,  {^"+\)i"-^r%"=\^%") 
equals  10%''''  for  the  width  of  steps  in  the  second  story. 

Risers.  The  risers  for  the  first  story  are  to  be  dressed  up 
neatly  to  1",  and  in  the  flight  to  the  attic  they  are  to  be  dressed 
8'''  wide.  If  the  risers  are  to  be  tongued  }>i,"  into  the  step  as 
shown  at  B,  Fig.  7,  then  the  width  of  rise  will  be  increased  3^^^, 
or  7J^  wide  for  the  first  flight  and  %%''  for  the  second  flight. 
Should  they  be  joined  as  at  the  external  angle  F  and  internal 
angle  iif  tongued  into  the  step  above  and  below,  then  the  width  of 
rise  would  be  minus  the  thickness  of  step,  plus  the  depth  of 
tongue  above  M" ,  and  also  the  tongue  below  J^''''  equals  (1" — IM''^ 
=Wi."-VW^W=-'o}i")  for  the  net  width  of  rise  ^%",  and 
the  step  would  be  increased  in  width  to  the  back  of  rise  as  shown. 

The  Circular  End  Steps  can  be  laid  off  on  the  ground 
plan.  From  the  center  with  the  dividers  strike  the  curves  and 
lay  off  the  miters.  Or  lay  off  the  plan  on  thick  paper  and  prick 
through  on  to  the  stuff  for  steps  and  trace  the  curves  on  the  steps. 
For  a  guide,  cut  sight  holes  through  the  paper  at  different  points 
••\ong  the  edge  of  steps  so  the  drawing  may  l)e  easily  regulated  on 
the  step.  The  system  of  patterns  shown  and  explained  for  Fig. 
10,  Plate  23,  will  be  found  the  most  convenient  for  a  large  stair 
shop. 

The  mitering  of  steps,  risers  and  glueing  the  same  has  been 
explained  in  connection  with  Plate  22. 

After  the  panel  work  under  the  first  flight  is  prepared,  steps  nosed 
and  together  with  the  scotia  cleaned  off,  the  nosings  let  into  the  wall 
strings,  cylinders  glued  on  to  the  long  front  strings,  and  joinis 
dressed  off,  the  work  is  ready  for  the  building. 

If  the  work  has  to  be  handled  a  good  deal  in  shipping,  then  cover 
the  miters  on  the  steps  and  risers;  also  protect  the  exposed  joints  of 
cylinders  and  strings.  The  cylindrvs  that  are  glued  to  the  string 
should  be  well  braced  before  leavia.^  ^o  shop  for  the  building.  The 
height  of  the  platform  may  be  markcu  uu  the  cylinder  before  leaving 
the  shop.  When  the  stairs  are  stepped  up  take  the  level  length  and 
enter  them  in  the  order  boolc  when  returned  to  the  shop.  Also  have 
blocks  well  fastened  in  the  walls  at  the  termination  of  rail  so  that  the 
rail  and  rosette  may  be  securely  fastened  to  the  wall.  Also  at  the. 
starting  and  landing  of  all  flights,  see  that  blocks  are  cut  between  the 
studs  and  the  walls  plugged  that  solid  railing  may  be  had  for  the 

6  3iS6  111  0  O  t^  S 

Bracket  well,  underneath  the  stairs,  always  have  the  grain  of 
wood  perpendicular  to  the  step.  Keep  the  ends  of  brackets  V^"  above 
the  lower  edge  of  carriage  or  bearer  so  that  in  case  of  shrinkage  the 
ends  of  brackets  would  not  break  the  plaster. 

In  the  first  flight  to  the  platform  two  3"X4"  scantling,  AA,  Fig. 
1,  Plate  25,  are  shown  placed  against  the  front  string,  and  rough 
brackets  on  the  opposite  side  from  the  string,  the  center  bearer  Is 
bracketed  on  both  sides  to  distribute  the  weight  equally,  and  also 
deafen  the  walking  line.  , 

In  the  flight  to  the  attic,  there  Is  no  support  from  a  panel,  as  in 
the  first  flight;  therefore,  double  the  center  and  also  the  outer  bearer 
and  bracket  the  same  as  shown  for  the  first  flight  to  the  platform. 

Scantling  3"X4",  doubled  in  this  case,  will  give  ample  strength, 
but  will  deflect  in  time,  and  cause  the  plaster  to  crack. 

A  good  and  economical  way  to  prevent  the  bearer  deflecting 
whenever  it  can  be  done,  is  to  put  a  Vi'  rod  through  the  outer  bearer 
parallel  to  the  risers,  and  anchored  well  Into  or  through  the  wall; 


Plate  38.  129 

sive  the  rod  all  the  inclination  possible  from  the  lower  edge  of 
hearer  to  the  internal  angle  of  step  and  rise  on  the  under  side.  The 
rods  may  be  used  every  four  [4'  0"]  feet.  Also,  brace  well  between 
the  outer  bearer  and  the  wall  horizontallj'. 

Strength  of  hearers  underneath  the  stairs  to  prevent  tlw 
crackiim  of  plaster. 

At  Fig.  9,  Plate  23  is  shown  the  outer  bearer  for  the  Hisht  to 
the  attic,  Fig.  3,  Plate  35. 

For  stiffues.s  of  joist  to  prevent  tiie  cracliing  of  plaster,  Tred- 
gokl  allows  a  flexure  of  ^g  of  an  inch  for  every  foot  in  leugth. 
Mr.  R.  G.  Hatfield,  in  his  valuable  treatise  on  Tmpi^ueJ'se  Strains, 
recommends  ^  of  an  inch,  or  the  decimal  .03'^  per  foot  in  leugth 
for  a  full  load.  D,  Copet  Berg,  in  his  article  on  safe  buildiug,  in 
the  Americati  Archilcrt,  makes  use  of  the  same  constant,  stating 
the  deflection  should  not  exceed  0.03  of  an  inch  per  foot  of  span, 
or  else  the  plastering  will  be  apt  to  crack. 

The  stair-builder  should  know  how  to  calculate  the  dimen- 
sions of  his  beams,  to  suit  the  weights  likelj"  to  come  upon  the 
stairs.  Mr.  R.  G.  Hatfield,  in  his  work  on  Transverse  Strains, 
has  given  us  the  benefit  of  his  experiments  iu  the  weight  of  crowds 
per  superficial  foot.  He  states  the  greatest  load  to  be  provided 
for  is  70  lbs.  per  superficial  foot  for  a  croud.  We  will  now  see 
what  load  likely  to  come  on  the  bearers  iu  the  flight  to  the  attic  in 
this  case. 

For  the  dead  load  we  have : 

14  yellow  pine  steps  4j^  cubic  ft.  @  33  lbs.  per  ft.  =15 1  lbs. 

15  white  pine  risers  and  front  string,  say     4  cubic  ft. 
For  bearers  and  rough  brackets,     .         .13      "     " 

1? 
Equals  17  cubic  ft.  of  white  pine  @  28  lbs.,  cubic  ft.=^476  lbs. 

Plastering. 

The  soffit  measures  14'  6^'X3'  6''i-=50%'^  square  ft. 

50,75  square  feet  of  plastering   @    9   lb.  per  foot -456.75 

Walnut  rail  and  balusters,  say  3>g  cubic  ft.  @  33  lbs.— 110.00 

Total,     1193.75 

This  gives  us  1,193%'  lbs  for  the  dead  load.  Should  iron  be 
used  as  flitches  for  the  bearers,  or  rods  for  trusses  or  hangers, 
their  weight  should  be  added. 

For  the  live  load  we  will  use  Mr.  Hatfield's  constant  of  7(» 
lbs  per  superficial  foot.  The  horizontal  distance  between  the  trim- 
mois  is  m'  (5'^,  and  width  of  stairway  between  the  plastering  and 
hand  rail  eciuals  3'  3'^  then  10'  6'^  by  3''  3^''  equals  say  34  square 
feet  at  70  lbs  per  foot  [34 X'' 0=2, 380]  equals  3.380  lbs  plus  the 
dead  load,  [2.3S0  ^1.193?^=3, 573%]  equals  3,574  lbs  for  the  whole 
load  likely  to  come  tipon  the  stairs  uniformly  distril>uted. 

To  distribute  this  load  on  the  bearer  underneath  the  stairs, 
two  methods  may  be  considered.  First,  by  ]ilacing  one  l>earer  at 
the  outer  string  sufficiently  strong  to  take  up  one-half  the  whole 
load,  allowing  the  wall  to  take  up  the  other  half.  Second,  or  by 
using  a  center  bearer  which  wotild  divide  the  load  into  four  equal 
parts,  thus  giving  to  the  center  bearer  one-half  the  whole  load, 
and  the  outer  bearer  and  the  wall  each  one-fourth  the  whole  load. 
We  will  consider  the  former  method  in  this  case  as  the  most  eco- 
nomical. 

Rule  to  find  the  size  of  bearers  allowing  .03  of  an  inch  for 
every  foot  in  length  for  deflection.  Tredgold  is  quoted  as  good 
authority  among  engineers;  he  gives  a  formula  for  inclining  beams, 
and  is  formulated  there  by  Mr.  F.  E.  Kidder,  author  of  the  Arch- 
itects' and  Builders'  Pocket  Book. 


130  Plate  28. 

Formula  no.  1. 

BreadthXcube  of  the  depthXe. 

Safe  load  at  the  center= 


Length Xhorizontal  distance  between  supports 

Formula  No  2. 

Load xlongthXhorizontal  distance  between  supports. 

Breadlh= — 

Cube  of  the  depth Xe. 

e  is  a  constant  and  equals  for  white  pine,  83.  ' 
e  is  a  constant  and  equals  for  hemlock,  80. 
e  is  a  constant  and  equals  for  white  oak,  95. 
e  is  a  constant  and  equals  for  wrought  iron,  2,000. 

The  deflection  from  a  weight  uniformly  distributed,  is  to  the 
deflection  caused  bj'  the  same  weight  placed  in  the  center  as  5  is 
to  8;  or  in  other  words,  %  of  the  uniformly  distributed  load  will 
deflect  the  same  beam  to  the  same  extent  if  the  load  be  placed  at 
the  center.* 

Now  we  have  a  uniformly  distributed  load  of  3,574  lbs.  to  be 
divided  into  2  equal  parts  [3, .574-^-2=1, 787  Ibs.J  equals  1,787  lbs; 
allowing^  of  this  for  acenter  load,  equals  [( 1,787 x;5)-=-8=l, 1169 j 
or  say  1,118  lbs.  for  the  center  load  on  the  outer  bearer. 

Example.  fWhat  must  be  the  breadth  of  a  white  pine  bearer 
to  carry  a  load  at  the  center  of  1.118  lbs,?  The  length  of  bearer 
on  the  rake  being  14^5,  and  the  horizontal  distance  between 
supports  being  10^5,  and  the  depth  of  bearer  to  equal  G'^. 

Breadth  equals  (1.118Xl■4.;yX10.5^-f-6.3//x«-=9.6^^  equals 
9.6''''  by  6^''  deep,  or  say  lO^^'X^^^  malting  60^''  for  the  cross  sec- 
tion of  timber.  Then  by  placing  2  bearers  5^^X6^''  side  by  side  at 
the  outer  string,  and  by  bolting  and  spiking  them  together,  will 
give  the  area  of  cross  section  and  be  amply  .stiif  enough  to  carry 
the  load  and  not  deflect  a  sufficient  amount  to  injure  the  plaster- 
ing. In  this  case,  a  center  bearer  will  be  rr^iuired  to  nail  up  the 
brackets,  and  afford  nailing  for  t!ie  lath;  lighter  material  as  two 
jj//<^4//  scantling  spiked  together  will  be  ample. 

If  brackets  be  nailed  on  both  sides  of  the  bearer,  they  will 
deafen  the  steps  on  the  treading  line.  In  this  case  the  length  of 
bearer  is  I4..y  long,  and  at  .0:;  of  an  inch  per  foot  for  deflection, 
would  deflect  fl4.5^X.03=.4o.'5]  the  bearer  equal  to  .43.5  of  an 
inch;  this  decimal  reduced  to  sixteenths  would  equal  [,435X 
16=0  960],  very  near  -/^  t>f  ^"  iucli. 

if  tlie  bearers  be  kerfcd  in  from  the  upper  side  |  their  depth, 
and  oak  wedges  driven  in  tlie  kerfs,  so  as  to  give  tliem  a  camber, 
this  will  add  jL  to  their  stiffness  for  flexure.:]:  Very  dry  material 
shouhl  be  used  in  this  case  to  make  the  work  substantial. 

Stuff  for  bearers  should  be  kept  on  hand  perfectly  seasoned, 
for  it  is  impossible  to  make  substantial  work  without  good,  dry 
material.  Where  two  scantlings  are  thus  spiked  together,  reduce 
th(!  two  inner  edges  to  form  a  V  shape  so  the  plastering  nuiy  have 
a  chance  to  key,  , 

In  long  and  heavy  flights  iron  flitches  or  angle  irons  should 
be  bolted  to  the  bearers,  for  to  depend  all  together  on  Avood  for 
bearers  would  increase  the  width  of  front  string  too  much,  and 
give  to  the  stair-case  a  clumsy  appearance. 

*See  Nicholson's  Dictionary,  Vol  2,  Page  530. 

+NoTE.— The  student  will  notice  tiie  length  of  bearer,  14'. C",  and 
also  tlie  iioiizontal  dislam-c,  or  run,  K/.O",  has  been  substituted  for 
15.0",  and  11'  2",  ^howu  at  Fig.  9,  Plate  23. 

■,     iMicholbou  dictionary,  Vol.  ~,  Page  530. 


Pt-ATK  9.S.  isi 

A  stimip  iron  or  oast  iron  shoe  slionltl  he  nsecT  at  tiie  lower 
end  to  support  tlie  bearer  and  its  load.  Also  the  floor  joist  at  the 
lower  end  of  bearers  should  be  well  1>ridged,  for  whei'e  cracks 
show  in  the  plastering  nine  cases  out  of  ten  they  will  appear  there 
first. 

In  case  the  outer  bearer  be  flitched  with  wrought  iron  at  its 
center  the  scantling  may  be  reduced  in  size.  The  proportion  for 
the  thickness  of  iron  to  the  wooil  being  equal  to  one-twelfth. 

Suppose  we  try  two  white  pine  bearers  4^^  by  5^'  flitched  at 
the  center,  the  thickness  of  flitch  will  equal  one-twelfth  the  thick- 
ness of  the  two  bearers  (S^''),  which  equals  ^^  of  an  inch,  and  for 
the  depth  we  will  allow  43^^^,  or  half  an  inch  less  than  the  depth 
of  scantling  to  allow  for  shrinkage  of  timber  and  for  the  plaster 
to  key. 

AYe  will  first  find  the  safe  load  at  the  center  for  the  wrought 
iron  flitcli  by  Formula  Xo.  1. 

Safe  load  at  the  center='*^'^^-^^^'^^"=748.1  pounds. 
8X14.5X10,5 
which  equals  say  749  lbs  as  the  safe  load  for  the  iron  flitch. 
We  will  next  find  the  safe  load  at  the  center  for  one  of  the  white 
pine  bearers  4''''X5''',  hy  Formula  No.  1. 

Safe  load  at  the  centers  ^    — =2(59.3  pounds. 

14.5X10.5 
which  equals  2G9  lbs  as  the  safe  load  for  one  bearer. 

Then  the  two  ))earers  (2094-269=538  lbs),  will  equal  538  lbs, 
plus  the  safe  load  for  the  iron  flitch  (749  lbs),  which  (538+749= 
1,287  lbs)  equals  1,287  lbs  and  not  deflect  .03  of  an  inch  per  lineal 
foot.  This  over-runs  the  whole  load  [1,287—1,118=169  lbs]  at  the 
center  of  outer  bearer  169  lbs,  which  will  make  up  for  the  iron 
flitch,  the  weight  of  same  being  139  lbs. 

The  two  bearers  and  flitch  are  to  be  bolted  together,  let  the 
bolts  pass  through  the  center  of  the  pine  bearers,  for  the  stress  in 
the  fibers  of  wood  are  less  on  that  line,  it  being  the  neutral  axis 
between  the  tensile  and  compressive  stresses.  At  the  upper  ends 
the  bearers  should  be  well  spiked  to  the  trimmer,  but  on  account 
of  the  extra  weight  the  outer  bearer  must  be  supported  l)y  a  stirrup 
iron,  or  a  cast  iron  shoe  bolted  to  the  trinnner  at  the  lower  end, 
as  shown  at  Fig.  9,  Plate  23. 

The  resistance  of  wrought  iron  to  a  tensile  strain  equals  60,000 
lbs  to  the  square  inch,  a  factor  of  6  is  usually  allowed  for  safety, 
hence  10.000  lbs  per  square  inch  is  allowed  as  a  safe  working  load 
for  wrought  iron. 

In  this  case  then  a  stirrup  made  from  a  light  iron  bar,  say 
k'^^Xli  "will  be  more  than  enough  to  support  the  load  at  the  lower 
end.  The  area  of  cross  section  for  one  side  [V4'''X1''''=0.25] 
equals  0.25  square  inches,  plus  the  area  of  the  other  side  (0.'i5-|- 
0.25=0.50)  equals  for  both  sides  0.5  of  a  siiuare  inch. 

Then  10,000  ll)s  by  0.5  equals  5,000  lbs  as  the  safe  load  for  the 
stirrup  iron.  In  using  the  light  iron  the  ends  that  lap  over  the 
trimmer  had  better  bo  upset,  thus  increasing  their  stiffness.  In 
addition  to  the  stirrup  iron  the  bearer  can  be  well  spiked  to  the 
trimmer,  thus  insuring  good  and  substantial  work. 


133  Pi.ATK  29. 


PLATE   29. 

Plato  29.  [Scale.  M^^=l  foot].  Exhibits  a  simple  method 
h(/w  to  construct  the  face^mould  for  the  stcvlr-case,  Plate  25. 

Fig.  1.  Shows  the  23?a''>i  of  the  center  line  of  rail  for  the 
cyllncicr,  Fig.  1,  Plate  26. 

The  rise  is  7''^X'^^^^  tread,  with  6^''  for  a  radius,  and  O  as  a 
center,  draw  the  semi-circle  as  shown  by  the  dotted  line  for  the 
face  of  cyli'nder;  the  balusters  are2^^X2^',  and  the  bracket  is  \4^'' 
thick;  the  face  of  baluster  is  flush  with  the  face  of  bracket,  that 
will  locate  the  center  of  baluster  back  from  the  face  of  front 
string  %'''';  the  radius  for  the  center  line  of  rail  will  then  equal 
(i%^^.  Now  with  6H^^  for  a  radius,  and  O  as  a  center,  draw  the 
semi-circle  ACE;  through  O  draw  the  diameter  AE.  Draw  the 
rectilineal  parallelogram  ABDE  to  tangent  the  curve  at  the 
points  A,  C  and  E.  Prolong  tangents  JBA  and  DE  indefinite 
towards  3  for  direction  of  straight  rail;  draw  OC  parallel  with 
AB  for  the  two  square  parallelograms  ABCO  and  EDCO  on 
plan.  The  face  of  No.  15  and  18  rise  is  5%^'  from  tlie  spring  of 
cylinder  as  shown. 

Pig.  2.  Shows  the  length  of  tangents  in  elevation;  the  t<m- 
gents  as  developed  from  plan,  are  folded. 

Let  XX  indicate  the  edge  of  drawing  board;  make  AB  equal 
AB  on  plan,  Fig.  1;  draw  AC  and  BD  perpendicular  to  XX; 
elevate  Nos.  15,  16,  17  and  18  rise  and  tread,  keeping  the  face  of 
No.  15  and  18  rise  5%^''  from  the  spring  line  AC  as  shown.     '• 

From  the  external  angle  of  No.  15  and  18  rise,  draw  the  true 
inclination  of  rail,  cutting  the  perpendiculars  from  A  and  J3  at  ^ 
and  F,  and  also  at  Cand  P;  prolong  the  inclination  to  intersect 
at  G.  Draw  G^i?  parallel  to  XX,  cutting  BD  at  K;  dra^v  EL 
indefinite  and  parallel  to  XX,  cutting  BD  at  M;  then  MK  is  the 
height  for  the  lower  wieath-piece,  and  HC  is  the  height  for  the 
upper  wreath  piece.  As  the  pitcl*  to  and  from  the  platform  is  the 
same,  the  two  heights  will  be  equal;  draw  FJ  and  PQ  parallel  to 
XX;  draw  iTJ"  prolonged;  then  EF  and  KJ  show  the  increased 
length  of  tangents  AB  and  BC  on  the  cutting  plane. 

Make  EL  equal  the  chord  AC  on  plan,  Fig.  1;  parallel  with 
BD  draw  the  half  width  of  rail  Y^W],  cutting  FE  and  KJ  At  4 
and  3;  from  K,  and  at  right  angles  to  EG,  draw  Kb\  also  from 
E,  and  at  right  angles  to  KJ  prolonged,  draw  E  6;  make  JN 
equal  JH. 

Bevels.  The  dotted  line  R  0  indicates  a  gauce  line  drawn 
parallel  to  XX;  draw  9  T  perpendicular  to  XX,  and  equal  to  the 
radius  OC,  Fig.  1;  make  0  7  equal  if  5;  also  make  9  8  equal  J576; 
draw  T  7  and  T  8  prolonged  to  edge  of  board;  the  bevels  are 
found  in  the  angles  at  7  and  8. 

Fig.  3.     Shows  hoio  to  construct  the  face-mould. 

Draw  BP' indefinite:  make  BA  equal  EF  in  elevation,  Fig. 
3;  with  A  as  a  center,  and  the  distance  LH,  Fig.  3,  for  a  radius, 
draw  arc  at  C;  again,  with  B  as  a  center,  and  KJ,  Fig.  3,  for  a 
radius;  draw  arc  intersecting  at  C;  join  BC;  parallel  with  BC 
and  BA.  draw  AO  and  CO  for  the  parallelogram  OABC  on  the 
cutting  plane. 

Proof.  The  diagonal  OB  must  equal  the  distance  LN,  Fig. 
S,  if  so,  the  angle  of  tangents  at  JB  must  be  correct.     Make  AJ 


Pr.ATK  29.  133 

equal  FG,  Fig.  3;  draw  JO  for  the  direction  of  minor  axis;  make 
O  2  equal  OC,  Fig.  1  for  the  length  of  semi-minor  axis;  make  3 
?,  and  2  4  each  equal  the  half  width  of  rail  [2U^^\-  Let  A  5  and 
A  6  each  equal  K  3,  Fig.  2;  also  make  C  7  and  C  8  each  equal  F 
4.  Fig.  2;  prolong  shank  6^^  from  A  to  P.  Make  joints  at  JP  and 
C  at  right  angles  to  BP  and  BC;  draw  6  9  and  5  10  parallel  to 
AP  for  the  shank.  Now  pivot  the  trammel  in  0,  with  the  arms 
XX  at  right  angles  to  0  2;  then  with  the  rod,  set  from  pencil  to 
minor  pin  the  distancer  O  3;  place  the  pencil  in  the  point  at  7,  and 
drop  the  pins  in  the  grooves,  then  fasten  the  major  pin,  and 
trace  the  curve  5,  3,  7,  for  the  concave  side  of  mould.  Again,  set 
from  pencil  to  minor  pin,  to  equal  the  distance  O  4,  then  place  the 
pencil  in  the  point  8,  and  drop  the  pins  in  the  grooves  and  fasten 
tlie  major  pin,  then  trace  the  curve  for  the  convex  side  of  mould 
througli  the  points  8,  4,  6;  the  curve  for  the  center  line  is  drawn 
in  the  same  way. 

At  sections  D  and  iVthe  tangent  lines  are  shown  carried  across 
the  joints  intersecting  the  dotted  gauge  line.  At  D  the  bevel 
found  in  the  angle  at  7,  Fig.  2,  is  applied  through  the  intersection. 
At  JVthe  bevel  found  in  the  angle  at  8,  Fig.  2,  is  applied  through 
the  center  of  plank.  It  will  be  observed  the  bevel  as  applied  at 
section  D  will  pitch  the  joint  at  C  up,  while  the  bevel  as  applied 
at  section  N,  will  pitch  the  shank  at  P,  down,  thus  showing  the 
wreath-piece  is  intended  to  land  on  tlie  platform  for  a  right  hand 
raii;  for  the  wreath-piece  off  the  platform  turn  the  stock  of  bevel 
reverse  to  what  is  shown. 

The  sliaded  parts  at  section  D  and  JVshow  the  thickness  and 
width  of  plank  required  to  saw  out  the  crook  and  the  amount  of 
over  wood  to  be  removed  in  the  formation  of  wreath-piece. 

Fig.  4.  Shows  the  plan  of  the  center  line  of  rail  for  the 
cijlinder  starting  from  the  level  to  rake,  Fi<j.  2,  Plate  26". 

The  dotted  line  indicates  the  face  of  cylinder,  the  radius  Is 
r/',  the  solid  line  shows  the  center  of  baluster  or  the  center  line 
of  rail,  the  radius  of  which  is  ()%^'.  Then  with  O  as  a  center 
and  OA  (6%)  for  a  radius,  draw  the  semi-circle  ACE.  Through 
O  draw  the  diameter  AE;  draw  the  rectilineal  parallelogram 
EDBA  to  tangent  the  curve  at  EC  and  A;  draw  OC  at  right 
angles  to  AS  for  the  parallelograms  OCDE  and  OCBA  on  plan; 
prolong  tangents  DE  and  BA  to  the  right  for  the  direction  of 
straight  rail.  The  face  of  No.  2  rise  is  shown  located  3^^  from 
the  spring  of  cylinder,  the  rise  is  8''^  and  tread  9''''. 

Fig.  5.  Shows  the  elevation  and  development  of  tangents 
J'ro)ii  Flcji,  Fig.  4. 

Ill  this  case  let  it  be  observed  the  tangents  are  spread  out  or 
unfolded  from  the  plan.  In  the  former  case,  Fig.  2,  they  are  shown 
folded,  only  two  perpendiculars  being  drawn.  This  is  done  to  give 
the  learner  a  clear  idea  how  to  get  the  correct  height  *  of  each 
wreath-piece. 

Let  XX  represent  the  edge  of  draft  board,  make  ED,  DC, 
CB  and  BA  equal  the  tangents  ou  plan.  Fig.  4;  perpendicular  to 
XX  draw  AF,  BG,  CH,  DJ  and  EK  indefinite.  Now  elevate 
the  risers  and  treads,  keeping  the  face  of  No.  2  rise  3^^  from  the 
spring  line  EK,  as  shown.  Through  the  center  of  baluster  00, 
draw  tlie  inclination  of  the  underside  of  rail,  parallel  with  the- 
underside  of  rail  draw  the  center  of  rail  prolonged,  cutting  the 

*The  student  must  be  careful  to  obtain  the  exact  height  in  the 
elevation  to  have  the  wreath  rail  the  proper  height,  as  the  drawing 
may  be  correct  in  every  other  particular,  and  a  mistake  in  the  height 
will  spoil  the  wreath. 


134  Plate  9,9. 

spring  lino  at  K  and  also  DJ  at  P.  From  A  to  F  set  up 
the  lieiglit  of  half  a  rise  (4^^)  and  the  half  depth  of  rail  1%^^  addi- 
tional, (4^''-f  1;?^^^=53^)  equals  5'%^^  for  the  center  line  of  level 
rail.  Parallel  with  XX  draw  FR  prolonged,  cutting  the  perpen- 
dicular from  B  at  G;  draw  GP  prolonged,  cutting  the  perpendic- 
ular from  C  at  iZ"  and  also  the  spring  line  XK"  at /S,  From  iif 
and  parallel  to  XX,  draw  HT,  cutting  the  perpendicular  from  D 
at  Z7,  then  HR  is  the  height  for  the  level  wreath-piece  and  TK 
is  the  height  for  the  raking  wreath-piece.-  Prolong  KF  to  inter- 
sect HT  at  N.  From  K  and  parallel  to  XX  draw  kj  prolonged, 
Make  KW  equal  the  chord  EC,  Fig.  4.  From  U  and  at  right 
angles  to  NK  draw  U,  2.  From  J'and  at  right  angles  to  HP  pro- 
longed, draw  J  3.  Make  R  Y  equal  the  chord  CA,  Fig.  4.  Par- 
allel to  DJ  draw  tlie  half  width  of  rail,  cutting  the  inclination  of 
tangents  KF  at  4,  and  also  the  tangent  HF  at  5. 

Bevels.  Draw  the  dotted  line  6  7  parallel  to  XX;  perpen- 
dicular to  XX,  draw  6  9  equal  to  the  radius  OC,  Fig.  4;  make  6 
8  equal  U  2;  make  6  7  equal  J  3;  draw  9  8  and  9  7  prolonged  to 
edge  of  board  for  the  bevels  required  for  the  inclining  wreath- 
piece;  also  the  angle  GHR  gives  the  bevel  for  the  level  wreath- 
piece  at  the  shank. 

Fig.  6.     Shows  the  face-mould  for  the  level  u-rcath-picce. 

Draw  BF  indefinite;  make  BA  equal  BA  on  plan;  draw 
BC  at  right  angles  to  BF,  and  equal  to  GH,  Fig,  5;  draAV 
CO  and  AO  parallel  to  BA  and  BC  for  the  rectilineal  parallelo- 
gram ABCO. 

Proof.  If  the  diagonals  AC  and  BO  equal  the  distance  Hy, 
Fig,  5,  the  parallolograra  is  correct,  and  OC  is  the  semi-minor 
axis,  and  OA  is  the  semi-major  axis  of  the  elliptic  curve  for  the 
center  of  mould.  Make  AP  equal  6^'' lor  length  of  shank;  make 
jciint  at  P  square  to  BF;  make  C2  and  C  3,  each  equal  the  half 
width  of  rail  [214'^'J;  make  A  4  and  A  5,  each  equal  P. 5,  Fig.  5; 
draw  4  6  and  h  7  parallel  to  AF  for  width  of  shank.  Now 
pivot  Ihe  trammel  at  O,  and  set  from  pencil  to  minor  pin  the  dis- 
tance O  2,  and  from  pencil  to  major  pin  set  to  the  distance  0  4, 
and  trace  the  curve  from  2  to  4,  for  the  concave  side  of  mould. 
Again,  set  from  pencil  to  minor  pin  the  distance  O  3,  and  from 
pencil  to  major  pin  to  equal  the  distance  0  5,  then  trace  the  curve 
from  3  to  5,  for  the  convex  side  of  mould;  proceed  in  like  manner 
to  trace  the  center  line  if  required. 

In  trafing  the  curves  for  tliis  mould,  the  string  will  answer  to 
draw  tlie  elliptic  curve,  see  Fipr.  S,  Plate  5.  As  the  dilference  between 
tlie  two  axiri  Is  so  little,  the  curves  may  be  drawn  from  different  cen- 
ters on  tlie  niaior  axis  with  the  compasses  near  eiioufrli  for  practice. 
The  minor  axis  OC  gives  the  joint  at  C,  and  is  at  right  angles  to  tan- 
gent BC. 

At  section  D  the  tangent  is  shown  carried  across  the  joint  square 
to  the  face  of  crook,  and  intersecting  the  dotted  line;  the  bevel 
found  in  the  angle  at  H,  Fig.  5,  is  shown  applied  from  the  face  of 
crook,  through  the  c(  nter  of  plank  to  pitch  the  joint  at  C  up.  At 
section  iVthe  tangent  is  squared  across  the  joint,  intersecting  the 
dotted  line;  the  block  pattern  is  centered  at  the  inlersection,  and 
applied  square  to  the  face  of  plank,  thus  allowing  the  shank  AF 
to  have  a  horizontal  position;  the  shaded  part  shows  the  atnount 
of  over  wood  to  be  removed  at  the  shank. 

Fig.  7.  Shows  ihe  face-mould  for  the  wrcathr-jAecc  that  is 
inclhihig. 

Draw  DF  indefinite  and  at  any  convenient  place  on  the 
paper  that  will  suit  best  for  saving  the  material.     Make  BE  (ninal 


Plate  29.  135 

KP,  Fig.  5.  With  ^  for  a  center  and  the  distance  WT,  Fig.  5, 
for  a  radius,  draw  arc  at  C.  Again  with  D  for  a  center  and  HP, 
Fig.  5,  as  a  radius,  draw  arc  intersecting  at  C,  connect  DC.  Par- 
allel to  DC  and  DE,  draw  EO  and  CO  for  the  parallelogram 
OCDE  on  the  cutting  plane. 

Proof.  The  diagonal  OD  must  equal  the  distance  SW,  Fig. 
5.     If  so  the  angle  of  tangents  at  D  must  be  correct. 

Make  EJ  equal  FN,  Fig.  5,  draw  OJ  for  the  direction  of 
minor  axis.  Make  O  2  equal  the  radius  OC,  Fig  4  (6%^^).  Let 
2  3  and  2  4  each  equal  the  half  width  of  rail  (2}^).  Make  EQ 
and  E  5  each  equal  P  5,  Fig.  5.  Also  make  C 1  and  C8  each 
equal  P  4,  Fig.  5.  Now  pivot  the  trammel  in  O  with  the  arms  at 
right  angles  to  O  2  and  proceed  to  trace  the  curves  for  the  concave 
and  convex  sides  of  mould  as  described  for  Fig.  3. 

From  E  add  &"  for  straight  wood  to  P  for  shank.  Make 
joints  at  P  and  C  at  right  angles  to  the  tangents  DE  and 
DC,  draw  6  9  and  5  10  parallel  to  EP  for  the  width  of  shank. 

The  sections  at  N  and  D  show  the  application  of  bevels. 
The  bevel  at  iVis  found  in  the  angle  at  7,  Fig.  5.  and  the  bevel  at 
D  is  found  in  the  angle  at  8,  Fig.  5;  as  applied,  they  sliow  the 
correct  position  of  wreath-piece. 

Fig.  8.  Shows  the  plan  of  the  center  line  of  rail  for  the 
'■'  ral:c  to  level  ttt'jst"  landing  in  the  third  story,  slioion  at  Fi>j.  3, 
Plate  26. 

The  dotted  line  indicates  the  face  of  cylinder,  the  radius  being 
G'''.  The  solid  line  shows  the  center  of  rail,  and  is  struck  with  a 
radius  of  (3%^^  from  the  center  O. 

Through  the  center  0,  draw  AE  indefinite,  enclose  the  semi- 
circle ACE  with  the  rectilineal  parallelogram  ABDE;  draw  OC 
at  right  angles  to  AE,  and  we  have  the  two  square  parallelograms 
OABC  m\A.  OCDE  on  plan;  now  AB  and  ^Care  the  tangents 
for  tlie  inclining  wreath-piece,  and  ED,  DC  are  the  tangents  for 
the  wreath-i)iece  on  the  level;  prolong  BA  and  DE  to  llie  left 
for  the  direction  of  straight  rail. 

*Tlie  face  of  first  rise  outside  the  cylinder  is  No.  14,  being 
3'^  from  the  spring  line;  the  face  of  No.  15  rise  will  then 
extend  into  the  cylinder  6^^. 

Fig.  9.  Shous  the  elevation  of  tan(j€iits;  in  tliis  case  Oiey 
(trc  fiihled  similar  to  tliosc  at  Fig.  2,  the  shaded  part  shows  the 
twist  of  raH. 

Let  XX  indicate  the  edge  of  drawing  hoard.  Make  AB 
e(|ii:il  AB,  i''ig.  S,  ft)%^^];  draw  AC  and  BD  perpen<licular  to 
XX,  and  of  indelinite  lengtli;  now  elevate  Nos.  13,  14  and  15 
treads  and  risers,  keeping  the  face  of  No.  14  rise  'd^^  from  the 
spring  line  AC  as  shown.  Through  the  center  of  baluster  00, 
draw  the  inclination  of  the  under  side  of  rail;  parallel  with  the 
under  side  of  rail  draw  the  center  of  rail,  cutting  the  perpendicu- 
lars AC  and  BD  nt  E  and  h;  the  top  of  No.  15  rise  gives  the 
tloor  line;  from  the  floor  line  set  up  4'^  to  the  under  side  <)f  rail, 
and  the  half  depth  of  rail  [I  ?s''']  nioie,  making  5-?;,'^''  to  the  center 
of  rail  at  J\  draw  JK  parallel  to XX.  From  h  and  E,  diaw  AZ/ 
and  EM  prolomred;  bisect  LJ  at  n;  draw  nP  parallel  to  XX, 
draw  pL  prolonged;  join  Kn:  then  Mp  is  the  height  for  the 
inclining  wreath-piece,  and  nJ  is  the  heiuht  for  the  wreath  piece 
on  the  level;  prolong  Eh  to  intersect  np  prolonged  at  R.     From 

*To  rorve.'jpond  with  lliat  at  Plate  2G.  this  should  read  27s"  indteud 
of  3".    Also  the  same  at  Fig.  4.  ,^ 


136  Platp:  29. 

E,  aud  at  right  angles  to  pL,  draw  JE  6;  from  p,  and  at  right 
angles  to  JEIi,  draw  p  7;  make  Ly  equal  Ln;  make  EQ  eciual 
the  chord  AC,  Fig.  8. 

Parallel  with  BD  draw  the  half  width  of  rail,  cutting  Eh  at 
3  aud  LP  at  4,  and  also  nk  at  .5.  The  bevel  ^<hown  at  0  indicates 
tlie  point  of  pitch-board  at  the  center  of  buhister,  giving  the  incli- 
natiou  of  the  underside  of  rail. 

Bevels.  The  dotted  line  8  0  indicates  a  gauge  lino  parallel 
with  XX.  Perpendicular  to  XXdraw  STand  ecivuil  to  the  radius 
0C(6M'')  Fig.  8.  Make  /S  10.  equal  Pi.  Fig.  9.  Make  iS  12, 
equal  ^6.  Fig.  9.  Make  /S  8,  equal  2iJ,  Fig.  9.  Draw  TV^,  T 
10,  and  T8,  prolonged  to  edge  of  board  for  the  bevels  as  shown. 

Pig.  10.  Shows  the  face-mould  for  the  wreuth-jnecc  land- 
ing. 

Draw  BP  indefinite;  make  BA  equal  Eh  in  elevation  Fig. 
9.  With  A  for  a  center  and  Qn,  Fig  9.  as  a  radius,  draw  arc  at 
C.  Again  with  B  for  a  center  and  LP,  Fig.  9,  as  a  radius,  draw 
arc  intersecting  at  C,  connect  BC.  Parallel  with  tangent  BC 
aud  BA  draw  the  radial  lines  AO  aud  CO,  tonning  the  parallelo- 
gram OABC  on  the  cutting  plane. 

Proof.     The  diagonal  BO  must  equal  the  distance  QY,  Fig. 

9.  If  so,  the  angle  of  tangents  at  B  is  correct. 

Make  AJ  equal  hR,  Fig.  9,  draw  OJ  tor  tlie  direction  of 
minor  axis,  make  O  2  equal  DC,  Fig.  8,  make  2  3  aud  3  4  each 
equal  the  half  width  of  rail  (3k'^0-  Make  A  5  and  A  6  each 
equal  P  4,  Fig  9.     Let  C  7  and  C  S  each  equal  h  3,  Fig.  9. 

Xow  pivot  the  trammel  in  the  center  at  0.  with  the  arms  XX. 
at  right  angles  to  the  semi-minor  axis  0  2.  Tiien  set  from  pencil 
to  minor  pin  on  the  trannuel  rod  the  distance  O  3.  Now  i)laco 
the  pencil  in  the  point  at  7  and  drop  both  p  us  in  the  grooves, 
then  fasten  the  major-pin  and  trace  the  curves  through  the  points 
7,  3,  5,  for  the  concave  side  of  mould.  Again  set  from  pencil  to 
minor  pin  the  distance  O  4.  place  the  pencil  in  the  point  at  8  and 
drop  both  pins  in  the  groo\  es,  then  fasten  tht  major-pin  and  trace 
the  curve  through  the  points  8,  4,  6,  for  the  convex  side  of  mould. 
Set  off  6^''  from  A  to  P  for  length  of  shank.  Make  joints  at  P 
and  C  at  right  angles  to  the  tangents  BP  and  BC.  Draw  5  9 
aud  6  10  parallel  to  AP  for  the  width  of  mould  at  the  shank. 

The  section  at  D  shows  the  bevel  taken  from  the  angle  at 

10,  Fig.  9,  and  applied  through  the  center  of  plank;  the  section  at 
N  shows  the  bevel  taken  from  the  angle  at  13.  Fig.  9,  and 
applied  from  the  face  of  crook  through  the  center  of  plank,  so  as 
to  pitch  the  shank  down,  as  required. 

Fig.  11.  Shotvs  the  face-mould  for  the  uyreatlypiece  o?i  the 
level. 

This  face-mould  may  be  drawn  with  the  compasses  from 
different  points  on  the  major  axis  line  OE;  the  parallel  sides  ED 
and  OC,  of  the  parallelogram  equal  the  radius  DC,  Fig.  8,  and 
the  parallel  sides  OE  aud  CD  e<iual  Kn,  Fig.  9. 

The  bevel  at  section  D  is  shown  in  the  angle  at  8,  Fig.  9,  and 
is  applied  so  as  to  pitch  the  joint  at  C  down;  at  section  N  the 
square  is  applied,  thus  allowing  the  shank  to  conform  to  the  Hue 
of  floor.  The  block  pattern  is  shown  applied  at  right  angles  to 
the  lines  made  from  the  bevel  and  trj^  square,  showing  the  twist 
of  wreath-piece  in  the  crook. 

Pig.  12.  Shoivs  the  plan  of  turnout  corrcfspondiny  to  Fig. 
4,  Plate  26,  lohich  is  supposed  to  be  made  on  heavy  building 


Plate  29.  ]?.T 

paper,  and  aftei'  the  steps  are  got  out,  the  drawing  is  rolled  up, 
and  when  the  patterns  are  required  for  the  rail,  the  face-mould 
is  laid  off  on  the  paper. 

The  tangents  HF  and  JVproduced,  and  the  position  of  risers 
all  correspond  to  Fig.  4,  I'late  26.  Draw  HO  and  JO  parallel  to 
FJ&vidFH,  forming  the  parallelogram  OHFJ;  prolong  tangent 
jy  indefinite;  from  iif  draw  iJC  at  right  angles  to  JC;  the  face 
of  No.  3  rise  is  shown  iH^^  from  the  spring  of  curve. 

Fig.  13.    Shoirs  the  cleiHttion  of  tangents. 

Let  XX  indicate  the  floor  line.  Make  FH  and  FJ  equal 
the  tangents  FH  and  FJ  on  plan,  Fig.  12.  Parallel  with  FD, 
draw  JG,  cutting  the  inclination  of  the  center  line  of  rail  at  Q, 
prolong  ED  to  intersect  JCr  at  L,  then  LQ  equals  the  height  the 
wreath-piece  will  rise  in  the  curve  at  the  center  of  wreath-piece. 

Make  LM  equal  the  chord  HJ,  Fig.  12;  let  X>JV equal  J'C, 
Fig.  12.  From  iVand  at  right  angles  to  QD  prolonged  draw  NK; 
draw  HP  parallel  to  FD.  Make  J*  2  equal  iif  2  on  plan  for  the 
point  of  miter.      Make  Z/Tt qual  FO,  Fig.  12. 

Bevels.  Let  iS  5  indicate  a  gauge  line  parallel  to  XX. 
Perpendicular  to  XX  draw  SR  and  equal  to  HC,  Fig.  12.  Make 
(S  5  equal  the  hc'ujht  LQ.  Let  iS  6  equal  NK,  draw  R  5  and  R 
t>  prolonged  to  edge  of  board  XX.  Parallel  to  /S  5,  draw  the  hall' 
width  of  rail  (2J4^0«  cutting  the  hypotheuuse  of  bevels  at  T  and  8. 

Fig.  14.     Shoivs  the  face-mould. 

At  any  convenient  place  on  the  paper  draw  J'P  indefinite. 
Make  FJ  eciual  DQ,  Fig.  13.  With  J"  as  a  center  and  MQ,  Fig. 
13,  for  a  radius,  draw  arc  at  H.  Again  with  JF'as  a  center  and  FH, 
Fig.  12,  for  a  radius,  draw  arc  intersecting  at  .H";  draw  i^iiZ"  pro- 
longed to  equal  H2  on  plan.  Fig.  12.  Draw  HO  and  JO  parallel 
to  JVand  FH  for  the  parallelogram  OHFJ  on  the  cutting  plane, 
which  will  coincide  when  in  position  with  the  parallelogram 
OHFJ  on  pM\,  Fig.  12. 

Proof.  The  diagonal  FO  must  equal  the  distance  TQ,  Fig. 
13.     If  so,  the  angle  of  tangents  at  F  must  be  correct. 

Make  JTPetiual  6"  for  length  of  shank,  make  Joints  at  2  and 
P  at  right  angles  to  the  tangents  F  2  and  FP.  From  iif  and  at 
right  angles  to  FH  draw  a  line  indefinite.  Prolong  the  diagonal 
FO  to  intersect  the  line  from  H\  from  the  intersection  (not 
shown)  draw  the  radial  line  through  J^  prolonged  for  the  points 
of  contact,  or  the  connection  of  straight  with  the  curved  part  of 
mould. 

Make  P  C  and  P  13  each  equal  6  7,  Fig.  13.  Make  H4  and 
H  3  each  equal  5  8,  Fig.  13;  draw  13  7  and  6  8  parallel  to  JP; 
draw  3  1 1  and  4  12  parallel  to  H  2.  Now  the  intersection  (not 
shown)  is  the  point  to  pivot  the  trammel,  and  from  the  inter- 
section to  the  point  3  is  the  semi-major  axis  for  the  concave 
side  of  mould,  and  the  minor  axis  would  be  at  right 
:inglcs.  but  on  account  of  the  extreme  length  of  the  axis 
as  shown  at  J,  Fig.  13,  Plate  17,  it  would  be  attended 
with  too  much  trouble.  A  better  way  to  use  the  ordinates  as 
jireviously  explained,  and  thus  find  all  the  points  in  the  curve 
that  may  be  desired.  Or  points  may  be  found  on  the  diagonal 
FO",  through  wliich  the  curves  may  be  drawn  by  using  the  pliable 

'Tlit'fie  points  on  the  diagonal  sive  another  point  in  each  curve 
u  \\(\  :iiiswcrs  very  well  for  small  cylinders.  But  for  tlie  large  cylinders 
and  for  face-moulds  over  winders  more  points  in  the  curves  are 
retjuiied  for  a  correct  trace  of  the  face-mould.  These  three  points 
iiiiiy  be  found  on  the  proof  diagonal  in  elevation  for  any  wreath- 
l)iece  as  sliown  by  the  dots  on  the  line  YZ,  Fig.  2,  Plate  32,  for  all 
wreatli-picces  standing  over  a  quarter  circle  on  plan;  and  for  all 
wreatli  pieces  less  than  a  quarter  circle  the  points  are  found  on  the 
proof  diagonal  as  shown  at  Fig.  4,  Plate  24. 


1!^8  I*TATR   29. 

strip.  Tlius  return  to  the  elevation  Fig.  13,  draw  TQ,  make  L  3 
equal  0  5,  Fig.  13,  draw  ?,  4  parallel  to  LQ.  Now  return  to  Fig  14, 
nialve  0  5  equal  Q  4,  Fig.  13,  and  draw  tlie  proportional  line  H  5, 
draw  4  10  parallel  to  JffS,  make  5  9  equal  5  10.  Xow  williaplia- 
l)le  strip,  draw  the  curve  7,  9,  .",  for  tlie  concave  side  of  mould 
and  through  the  points  8,  10,  4,  draw  the  curve  for  the  convex  sidp 
of  mould,  and  tlirough  the  points  H  5,  J,  draw  the  center  line  of 
mould.  At  section  N  the  bevel  foinid  in  the  angle  at  5,  Fig,  13, 
is  shown  applied  from  the  face  of  crook  through  the  center  of 
plank.  At  section  D  the  bevel  found  in  the  angle  at  6,  Fig.  13, 
is  shown  applied  tlnough  the  center  of  planlc,  and  the  block  pat- 
tern is  applied  square  to  the  line  made  from  the  bevel,  thus  show- 
ing the  twist  of  wreath-piece  in  the  crook.  Observe  the  bevels  do 
not  cross  the  tangents  in  their  application.  The  shading  shows 
tlie  surplus  wood  to  be  removed,  and  also  the  thickness  and  width 
of  plank  required  to  saw  out  the  crook. 

Fig.  15.  Shows  the  easement  pattern  for  the  landing  of 
tlie  ftrst  flight.  IIov)  to  marTi  the  point  Fan  tlie  pattern  so  as  to 
cut  and  joint  the  rail  at  the  bench. 

Draw  a  tread  and  rise  and  floor  line  anywhere  on  the  draft- 
board;  through  the  center  of  baluster  XX,  draw  the  under  side 
of  rail.  Then  take  the  easement  pattern  already  made,  and 
apply  the  lower  edge  to  the  inclination  through  XX,  as  shown; 
now  slide  the  pattern  until  the  lower  edge  at  AB  will  equal  the 
distance  XQ,  [4^^J  Fig.  5 ;  then  mark  the  pattern  opposite  the 
landing  rise  at  center  of  rail,  as  shown  at  F,  and  we  have  5''''  to 
the  joint  at  Con  the  inclination  to  allow  when  cutting  the  straight 
rail.  And  from  F  to  J3,  parallel  with  the  floor  line,  we  have 
'M}i^^  to  allow  for  the  easement  when  cutting  the  straight  rail  for 
the  level.  At  1  is  shown  how  much  longer  the  long  baluster  is 
tlian  the  regular  short  baluster  for  the  first  flight;  4  5  shows  how 
much  longer  the  balusters  for  the  level  are  to  be  over  the  regular 
short  balusters;  at  2  and  3  the  difference  over  the  regular  short 
balusten-s  is  shown  for  these  two  odd  balusters. 

Figs.  8,  9  and  10,  Plate  28.  Shoivs  how  to  construct 
the  face-mould  over  a  quaHer  pace  xvindinrj,  so  as  to  form  two 
e'lsinfjs  in  the  wreath-piece,  thus  avoidimj  the  short  ramp 
usually  at  the  lov)er  end  of  wreath- piece. 

Fig.  8.  Shows  the  plan  of  quarter  cylinder  having  three 
winders  in  the  quarter  pace;  AB  and  BC  are  the  tangents  en- 
closing the  center  line  of  rail;  AD  and  CB  indicate  the  direction 
of  straight  rail;  OABC  shows  the  parallelogram  on  plan. 

Fig.  9.    tiliows  the  elevation  of  ta7igents. 

Let  XX  indicate  the  edge  of  drawing  board.  Make  AB 
'^  equal  AB,  Fig.  8.  Draw  AC  and  BD  perpendicular  to  XX  and 
of  indelinite  length.  Now  elevate  the  treads  and  risers,  keeping 
the  face  of  No.  9  rise  2^^  and  also  the  face  of  No.  13  rise  10^^ 
from  the  spring  line  AC;  through  the  center  of  baluster  00  and 
00  draw  the  under  side  of  rail;  parallel  with  the  under  side  of 
rail,  draw  the  cenler  of  rail,  intersecting  AC  at  E,  and  at  the 
upper  end  prolong  the  inclination  indefinite,  cutting  BD  at  H: 
draw  HE  prolonged  indefinite;  perpendicular  to  AF  draw  FD 
to  cut  EH  prolonged  at  Gr;  make  EJ  perpendicular  to  AC; 
make  EK  equal  the  chord  AC,  Fig.  8;  make  FL  equal  twice 
DH:  parallel  with  BD,  draw  the  half  width  of  rail,  cutting  EH 
and  FH  at  2  and  3;  ease  the  angle  at  E;  at  right  angles  to  ME, 
and  at  the  spring  of  easing,  draw  the  joint  line  4  5,  cutting  the 
center  of  straight  rail  at  6,  and  also  £rJ7  prolonged  at  7;  parallel 


Pt.aTR  29.  isy 

with  HE  prolonged,  draw  the  half  thickness  of  plank,  cutting  the 
joint  line  4  7  at  5;  from  5,  and  perpendicular  to  i?^  prolonged, 
draw  5  8,  cutting  HE  prolonged  at  N.  Now  NE  is  the  length 
required  for  the  shank  of  face-mould  at  the  lower  end;  the  shank 
of  mould  at  the  upper  end  may  be  any  length,  as  the  wreath- 
piece  contains  a  natural  easing. 

Bevels.  From  the  center  D,  draw  a  line  to  tangent  HG, 
and  intersect  HB  at  P;  join  PF;  the  angle  at  P  gives  the  bevel 
for  the  lower  end  of  wreath-piece;  again,  from  t!ie  center  J  draw 
a  line  to  tangent  FH  prolonged,  and  intersect  BD  at  Q;  join 
QE  for  the  bevel  required  at  the  upper  end  of  wreath-piece.  The 
bevel  shown  in  the  angle  at  5,  applies  from  the  joint  after  the 
sides  of  wreath-piece  are  worked  off  to  the  plumb. 

Pig.  10.     Sliovs  the  face-mould. 

Make  NEH  eqiml  NEH  Fig,  9;  with  S  as  a  center,  and  the 
distance  FK.  Fig.  9.  for  a  radius,  draw  arc  at  J";  again,  with  if  for 
a  center,  and  FH,  Fig.  9,  for  a  radius,  draw  arc,  cutting  at  F; 
chaw  JTH" prolonged;  parallel  with  EH  and  HF,  draw  FO  and 
EO  for  the  parallelogram  OFHE  on  the  cutting  plane. 

Proof.  The  diagonal  HO  must  equal  the  distance  LK,  Fig. 
9,  if  so,  the  angle  of  tangents  at  JFfmust  be  correct. 

Make  EG  equal  HG,  Fig.  9;  draw  GO  indefinite  for  the 
direction  of  minor  axis;  make  OC  equal  OC  on  plan,  Fig.  9; 
make  C2  and  C3  each  equal  the  half  width  of  rail  \l}4^^]\  make 
E  4  and  E  5  each  equal  H  3,  Fig.  9;  make  F  6  and  F  7 
each  equal  H  2,  Fig.  9;  make  joints  at  N  and  S  perpendic- 
ular to  the  tangents  HE  and  HF;  from  the  points  6,  7,  and 
5,  4.  draw  lines  for  the  straight  wood  parallel  to  the  tangents 
HS  and  HN  to  intersect  the  joints  at  8,  9,  and  10,  11;  now  draw 
the  curves  of  face-mould  in  the  usual  way. 

The  bevel  found  in  the  angle  at  Q,  Fig.  9,  is  shown  applied 
at  section  B;  and  the  bevel  found  in  the  angle  at  P,  Fig.  9,  is 
shown  applied  at  section  A;  the  block  pattern  is  shown  applied 
in  the  usual  way. 

Now  work  off  the  sides  of  wreath- piece  to  the  plumb,  then 
through  the  center  of  rail  section  draw  ab  as  shown  at  section  A; 
from  a  and  b  draw  lines  on  the  sides  of  wreath-piece  square  to 
the  joint,  then  mark  on  these  lines  from  tlie  joint  the  distance  N 
7,  Fig.  9.  Now  apply  the  bevel  shown  in  the  angle  at  .5,  Fig.  9, 
from  the  joint  and  through  the  points  just  found  on  the  sides 
of  wreath-piece  which  will  give  the  cripple  joint  5  4,  Fig.  9: 
a  section  of  this  joint  is  shown  at  D.  the  points  7  and  6  cor- 
respond to  the  two  centers  7  and  6,  Fig.  9;  after  the  cripple 
joint  is  cut,  then  carry  the  line  ab  across  the  joint,  and  also  the 
plumb  line  made  from  the  i)evel;  raise  up  the  distance 
7  G,  Fig.  9,  for  tlie  center  of  block  pattetn,  and  shape  the  easing 
square  from  the  joirit  last  made;  the  points  7  and  0  correspond  to 
the  two  centers  7  and  6,  Fig.  9.  Observe  a  piece  may  be  glued  on 
the  top  of  wreath-piece  to  accommodate  the  easing;  the  crook 
must  be  sawn  out  wider  on  the  concave  side  to  allow  the  block 
pattern  to  raise  up  the  required  height,  7  6,  Fig.  9.  This  method 
of  forming  the  unnatural  or  forced  easing  in  the  wreath-piece 
at  the  lower  end  is  not  preferred  by  the  author;  in  a  case  of  this 
kind,  when  the  inclination  of  pitches  is  less  steep  then  an  easing 
may  be  worked  on  the  shank  of  wreath-piece  and  carried  into 
the  twist  part  with  good  results.  At  Fig.  9,  the  parallelogram 
FHWZ  is  shown  projected  from  the  tangent  FHm  elevation. 

Some  prefer  in  this  way  to  find  the  angle  of  tangents  on  the 
oitting  jilane,  then  transfer  them  to  the  material  for  pattern  by 
using  a  bevel. 


140  Plate  SO. 


PLATE   30. 

Plate  30.  [Scale  M^^=l  foot].  Exhibits  how  to  cotistruct 
the  face-mould  ivhen.  the  risers  are  placed  at  any  point  in  the 
cylinder  without  reference  to  what  effect  they  viay  luwe  on  the 
wreath  part  of  rail  as  is  sometimes  the  case,  ivith  ordered  rails, 
and  also  in  the  capping  of  iron  balustrades. 

Pigs.  1  and  2.  Shoio  how  to  Und  the  length  of  tangents 
and  treatment  of  the  wreath  over  a  cylinder  12"  in  diameter  start- 
ing from  the  level  to  a  rake,  rvhen  the  face  of  No.  1  rise  is  1" 
outside  the  spring  of  cylinder,  ihe  balusters  are2''^2",  bracket 
%"  thick.  Then  the  radius  for  the  center  line  of  rail  will  equal 
6%'\  The  rise  is  8"  by  d"  tread.  The  size  of  rail  is  4}4"  by 
2%" .    The  rail  is  to  be  a  "■right-hand  rail." 

Fig.  1.     Shows  the  plan. 

From  the  center  O  draw  the  semi-circle  ACE  io  a  radius  of 
6%''''  for  the  center  line  of  rail.  Enclose  the  semicircle  "with  the 
rectilineal  parallelogram  ABDE,  draw  OC,  forming,  the  two 
square  parallelograms  OABC  and  OCDE.  Prolong  tangents 
BA  and  DEto  the  right  for  the  direction  of  straight  string.  The 
dotted  line  shows  the  face  of  outer  string.  The  face  of  No.  1 
rise  is  one  {1")  inch  outside  the  spring  of  cjiinder. 

Fig.  2.  Shows  the  elevation  of  tangents,  as  developed  from 
plan,  they  are  folded. 

Let  XX  indicate  the  edge  of  drawing  board,  make  AB  equal 
AB  on  plan,  Fig.  1,  (G%"},  draw  AE  and  BD  perpendicular  to 
XX,  elevate  No.  1  and  2  rise  and  tread,  keeping  the  face  of  No. 
1  rise  1"  from  the  spring  line  AE.  At  B  set  up  4^^  to  the  under- 
side of  rail  plus  the  half  thickness  of  rail  riys^''+4'''=5^<^^) 
equals  5%^''to  the  center  of  rail  as  BC;  draw  CF  parallel  to  XX. 

Through  the  center  of  baluster  00  draw  the  underside  of 
rail,  parallel  with  00  draw  the  inclination  for  the  center  line  of 
rail  to  intersect  AE  at  h. 

Let  it  be  observed  that  if  the  center  line  of  rail  Gh,  were 
prolonged  to  intersect  the  perpendicular  BD,  it  would  fall  below 
the  point  C,  and  as  the  point  C  is  a  fixed  point,  we  will  have  to 
assume  an  inclination  for  the  wreath-piece  different  from  the  reg- 
ular pitch  and  make  what  is  termed  a  "cripple  joint"  at  tlie 
shank  end  of  mould. 

Then  draw  CJ  for  the  assumed  pitch,  cutting  AE  at  K.  Tlie 
point  J"  is  not  arl)itrary,  the  stair-builder  can  use  his  judgment  as 
to  what  inclination  or  length  to  make  the  shank  JK.  At  C  is 
sliown  a  section  of  rail.  C  2  shows  the  increased  witltli  of  mould 
for  half  the  rail  at  the  center  joint.  In  the  angle  at  K  is  shown 
the  bevel  for  the  center  joint.  At  the  shank  joint  of  mould  the 
square  will  be  applied  because  there  is  no  spring  in  tliis  case. 

The  joint  at  J  is  made  at  right  angles  to  the  true  jiitch,  and 
the  bevel  shown  at  J"  gives  the  cut  for  tlie  cripple  joint  as  shown. 
Tlie  shaded  part  shows  the  curve  of  wreath-piece  flowing  into  the 
straight  rail.  In  the  hands  of  a  skillful  stair-builder  this  treat- 
ment of  the  wreath-piece  will  give  a  beautiful  twist  as  the  curve 
is  carried  more  into  tiie  shank. 

The  dotted  lines  drawn  parallel  with  CJ  show  the  thickness 
(5")  of  plank  required,  less  thickness  would  answer  by  taking  off 
the  corners  as  shown  at  section  N,  Fig.  5 ,  for  they  will  come  off 
in  moulding  the  wreath-piece. 


Plate  30.  141 

The  face-mould  for  this  wreath-piece  is  shown  at  Fig.  5. 

Figs.  3  and  4.  Repeats  Figs.  1  and  2,  only  the  former  is 
shown  for  a  wreath-piece  landing,  or  from  the  rake  to  a  level. 
The  face  of  No.  1(5  rise  is  one  inch  (f)  outside  the  spring  of  cyl- 
inder. The  tangents  AB,  BC,  CD  and  D.E7  coincide  with  those 
at  plan,  Fig.  1. 

Fig.  4.     Shoivs  the  elevation  of  tcmgents,  they  hcing  folded. 

Let  XX  indicate  the  edge  of  draught  board,  make  AB  equal 
AB,  J-jg.  3.  Draw  AE  and  BD  perpendicular  to  XX.  Elevate 
No.  15  and  16  treads  and  risers,  also  floor  line,  keeping  the  face  of 
No.  16  rise  1^'  from  the  spring  line  AE.  Draw  the  floor  line  OS. 
Through  the  center  of  baluster  00  draw  the  inclination  for  the 
underside  of  rail,  parallel  with  00  draw  the  center  line  of  rail 
intersecting  AE  at  h.  At  the  floor  line  /S  set  up  4'^  to  the  under- 
side of  rail  and  IM^^  more  or  o%^^  to  the  center  C,  then  Cis  a 
fixed  point.     Draw  Cr parallel  to  XX,  cutting  AE  at  W. 

Now  let  it  be  observed  that  if  the  true  inclination  Gh  were 
prolonged  to  intersect  BD,  it  would  raise  above  the  fixed  point  C, 
which  would  be  too  high,  so  we  will  make  a  cripple  joint 
at  the  shank  same  as  at  Fig.  2.  Now  in  drawing  this,  to  save 
time  draw  the  assumed  pitch  to  agree  with  that  at  Fig.  2,  and 
make  one  face-mould  answer  for  both  wreath-pieces. 

Then  make  CF  equal  FK,  Fig.  2.  draw  J^jff  parallel  to  XX, 
draw  CK  prolonged  to  intersect  GH  at  J,  make  the  joint  at  J 
at  right  angles  to  GJ.  The  bevel  in  the  angle  at  J  gives  the  down 
cut  for  tlie  cripple  joint,  the  bevel  in  the  angle  at  Cis  applied  at 
the  center  joint.  Parallel  with  BD  draw  the  half  width  of  rail, 
cutting  CK  at  2.  At  C  is  shown  a  square  section  of  rail  and  the 
dotted  lines  cutting  the  angles  of  block  pattern  are  drawn  parallel 
to  JC  and  give  the  thickness  of  plank  (4K^^'i  required  to  form 
the  twist.     Prolong  if2^  to  equal  the  chord  AC,  Fig.  o,  as  KU. 

Fig.  5.  Shows  the  face-mould  for  both  starting  and  land- 
ing. 

At  any  convenient  place  on  the  paper  draw  a  line  to  equal 
CKJ,  Fig.  4,  as  BAJ.  At  right  angles  to  JB  draw  AO  and 
BC  each  equal  to  AB,  Fig.  3.  Join  CO  for  the  rectilineal 
parallelogram  OABC  on  the  cutting  plane. 

Proof.  The  diagonal  OB  aiul  chord  AC  must  each  equal 
the  distance  UW,  Fig.  4.     If  so,  the  parallelogram  is  correct. 

As  all  the  angles  are  right  angles,  the  face-mould  will  be 
a  quarter  of  an  ellipse  with  the  joints  on  the  axis  lines.  Make  C 
2  and  C  3  each  equal  C2.  Fig.  4,  make  A  4  and  A  5  each  equal 
half  width  of  rail  i'~}4),  draw  4  6  and  5  7  parallel  to  AJ",  make 
joint  at  J  perpendicular  to  A  J.  The  dotted  line  at  J"  indicates 
the  overwood  required  for  making  the  cripple  joint. 

Pivot  the  trammel  at  the  point  Oand  sweep  the  quarter  ellipse 
in  the  usual  way.  The  section  N  shows  the  bevel  found  in  the 
angle  at  C,  Fig.  4,  applied  from  the  face  of  crook.  At  section  D 
the  try  square  is  shown  applied.  The  shaded  part  shows  the  thick  • 
ness  of  plank  and  the  width  at  joints  to  saw  out  the  crooks.  The 
center  point  at  section  D  should  equal  from  the  face  of  crook  the 
distance  4  J,  Fig.  4,  and  at  section  N  the  distance  3  C.  Fig.  4, 
from  the  upper  side  of  crook. 

Make  J  8  equal  Jh,  Fig.  4,  then  J  8  will  be  the  amount  to 
deduct  for  shank  when  cutting  the  straight  rail. 

In  the  two  elevations,  Fijrs.  2  and  1,  the  shader)  parts  show  thf> 
t\YO  wreath  pieces,  the  one  starting,  and  the  other  for  a  landinir;  it 
•will  be  observed  if  they  were  bolted  togetlicr  at  the  center  joint  C. 
they  would  answer  for  a  platform  twist.  The  quarter  turn  connectini: 
the  wreath-piece,  is  taken  from  plank  the  same  thickness  as  for  the 
straight  rail,  there  being  no  spring  bevel  required  at  the  shank  of 
quarter  turn. 


142  Plate  30. 

Figs.  6  to  10.  Shows  a  different  treatmeyit  of  a  landing 
and  stai'ting  twist. 

Fig.  6.  Shows  the  plan,  starting  from  the  level  to  a  rake 
similar  to  Fiq.  1. 

Ouly  in  this  case  the  face  of  rise  is  placed  on  line  with 
the  diameter  or  spring  line  of  cylinder,  the  rise  is  S'^'X^''^  tread, 
the  tangents  AB,  BC,  CD  and  DE,  coincide  with  Fig.  1. 

Fig.  7.     Shows  the  elevation;  the  tangents  arc  folded. 

Allow  BA  prolonged  to  indicate  a  base  line;  make  BA 
equal  tangent  AB  on  plan,  Fig.  6;  draw  AG  and  JBJ' perpendic- 
ular to  BA.  Now  elevate  No.  1  and  3  rise  and  tread,  keeping 
the  face  of  No.  1  rise  on  the  spring  line;  from  the  base  or  floor 
line  BA,  set  up  V^  to  the  under  side  of  rail  plus  the  lialf  thick- 
ness \l%^^\  of  rail,  \l%''+'^''=h%'']  equals  b%'^  to  L.  Draw 
LK  for  the  center  of  level  rail,  ttms  establishing  the  point  L; 
through  the  center  of  balusters  00,  draw  the  inclination  for  the 
under  side  of  rail;  parallel  with  00,  draw  the  center  line  of  rail, 
intersecting  AG  at  J".  From  L,  and  parallel  to  00,  draw  Lm. 
(In  tills  case,  Lm  happens  to  come  on  line  witli  the  upper  side  of 
rail.)  The  block  pattern  shows  the  section  of  rail  at  L.  Make 
shank  joint  at  pleasure,  say  at  2,  and  perpendicular  to  00. 

The  dotted  lines  show  the  thickness  of  plank  required  to  foi'Tii  llie 
twist,  the  thickness  of  rail  bciiis?  tr;iuKf'd  oil'  from  the  lower  side,  ajid 
all  the  over  wood  is  to  he  removed  from  the  top  side  of  crook  at  the 
shank;  1/  4  is  the  distance  from  the  lower  side  of  crook  to  center  the 
block  pattern  ati.  The  bevel  for  tlie  center  joint  is  shown  in  the 
angh!  atrn;  as  the  plank  in  this  case  is  canted  but  one  way,  only  one 
bevel  will  be  required;  the  try  square  will  apply  at  the  shank  joint; 
the  face-mould  is  shown  at  Fig.  10. 

Fig.  8.  Shows  the  2^toH  from  the  rake  to  a  level,  sliailar 
to  Fig.  3. 

Only  the  face  of  No.  16  rise  is  on  line  with  the  spring  of  cyl- 
inder. The  tangents  AB.  BC,  CD  and  DE,  and  also  the  tread 
and  rise  agree  with  Fig.  6. 

Fig.  9.  Shoivs  the  elevation  of  tangents  from  plan.  Fig.  s, 
they  arc  folded. 

Let  BA  prolonged,  indicate  a  base  line  or  line  of  floor;  per- 
pendicular to  BA,  draw  BF  and  AG;  elevate  No.  15  and  10 
rise  and  tread,  keeping  the  face  of  No.  10  rise  ou  the  spring  line 
AG. 

Tlirough  the  center  of  balusters  00  draw  the  inclination  for 
the  under  bide  of  rail,  parallel  with  00  draw  the  center  ot  rail 
intersecting  AG  at  J;  also  draw  the  upjier  side  of  rail /S :»,  to 
intersect  the  perpendicular  from  B  at  F.  From  the  Hooi-  line  set 
up  i^^  to  the  underside  of  rail  plus  the  half  thickness  (I;?h^^)  of 
rail  (4^^+l>^8^^=-53^'/)  ciuals  .^,?h^^  U>  L.  Draw  I,if  ))r.>h.nged 
and  parallel  to  BA,  draw  LM  ))aralhl  to  SF;  draw  MN  at 
right  angles  to  AG;  parallel  to  JBi^ draw  the  half  width  ot  rail 
(^'i'^),  cutting /S^  at  X.  The  block  pattern  is  shown  centered 
at  L,  the  dotted  line  shows  the  thickness  (»f  plank  reiiuired  for 
the  wreath  piece.  [-1%^^.]  Make  shank  joint  at  ])leasure,  say  ii  2. 
Let  L  U  equal  the  chord  AC  on  plan.  Fig.  8.  In  the  angle  at  L 
is  shown  the  bevel  for  the  center  joint. 

Fig.  10.    Shows  the  facc-mouhl. 

Make  BA  and  AJ vi\WA\  FZ  and  Z  3  Fig.  9.  From  A  and  B 
and  i>eri)endicular  to  jB  draw  BC  and  AO  each  equal  t(»  OC, 
Fig.  8,  for  the  rectilineal  parallelogram  OABC  on  the  cutting 
plane  or  plane  of  plank. 


Plate  30.  143 

Proof.  The  diagonal  BO  and  chord  AC  must  be  equal  and 
of  the  same  length  as  NU,  Fig.  9.  Make  joint  at  J  at  right  angles 
to  tangent  BJ.  Let  C  2  and  C  3  each  equal  Fx,  Fig.  9.  Also 
make  A  4  and  A  5  each  equal  the  half  width  of  rail  (2)^'^). 

Draw  4  6  and  5  7  parallel  to  AJ.  Now  pivot  the  trammel  in 
0  aud  trace  the  curves  for  the  face-mould  as  has  been  explained, 
riie  joint  at  C  is  ou  liue  with  the  major  axis  OC  in  this  case 
because  the  plank  is  not  sprung  and  the  angles  of  the  parallelo- 
gram on  plan  aud  face-mould  are  all  right  angles. 

The  section  at  N  show's  the  tangent  BC  carried  across  the 
joint  square  to  the  face  of  plank  and  the  dotted  line  run  on  from 
the  face  of  crook  equal  to  the  distance  L  4,  Fig.  9.  The  bevel 
found  in  the  augle  atL,  Fig.  9.  is  applied  through  the  intersection. 
At  section  D  the  full  thickness  of  rail  is  shown  gauged  from  the 
face  or  upper  side  of  crook  and  the  surplus  wood  at  the  shauk  is 
removed  from  the  under  side  of  crook. 

At  elevation  Fig.  7,  tlie  surplus  wood  at  the  shank  is  shown 
gauged  from  the  under  side  of  crook,  and  most  of  the  surplus 
wood  is  removed  from  the  top. 

It  will  l)o  o1xsorv(>d  that  if  the  wrf  ath-picce  for  Fior.  8  were  bolted 
to  tiiat  of  t'^ig.  tit,  it  ■would  answer  for  a  platform  twist,  the  face  of 
risers  hoins  on  line  with  the  spring  of  cylinder.  KJ  is  the  correct 
height  of  wreath-piece  from  center  to  center  of  rail. 

Make  J  9  on  face-mould  equal  J  2  in  elevation  Fig.  9,  for  the 
amount  to  be  deducted  tor  shank  when  jointing  the  straiglit  rail. 
The  quarter  turns  connecting  the  wreath-pieces  are  level  as 
described  for  Fig.  5. 

Figs.  11,  12  and  13.  Shows  a  third  inctlwd  how  to  obtain 
the  face-mould  when  the  risers  are  misplaced. 

Fig.  11.  Shows  the  plan  and  a,qrecs  icith  Fi(j.  8;  the  face 
of  No.  10  or  landiiKj,  rise  is  on  line  with  the  spring  of  cylinder. 

With  (yyi^^  as  a  radius  and  O  for  a  center  draw  tlie  semicircle 
ACE.  The  doited  line  indicates  the  face  of  cylinder.  Draw  the 
diameter  AOE,  draw  the  direction  of  straight  rail  from  A  aud  J5 
at  right  angles  to  AE, 

Fig.  12.  Shows  the  elevation  of  a  step  and  rise  and  incli- 
nation of  rail  from  ivhich  to  determine  the  length  of  tangents 
on  the  plan.     Tlie  rise  is  S^^  hy  d"  tread. 

Ijct  XX  iiulicate  tlie  edge  of  draught  board,  elevate  No.  1.5 
and  16  treatl  and  rise  ami  the  lloor  line  at  the  lauding.  From  A 
draw  the  spring  line  AE  indefinite.  Througlx  the  center  of 
balusters  00  draw  the  under  side  of  rail,  parallel  with  OO  draw 
tlie  center  line  of  rail  RJ  and  prolonged  indefinite.  From  the 
lloor  line  set  up  4^''  to  the  under  side  of  rail  and  the  half  thick- 
ness of  rail  l-'a^^niore,  or  5^tj^^tothe  center  of  rail  at  B  through 
B,  draw  a  line  parallel  to  the  floor  line,  cutting  the  inclination  for 
the  center  of  rail  at  Cand  prolonged  indefinite.  From  Cdraw  CD 
parallel  to  AB. 

Now  return  to  ])lan,  Fig.  11,  draw  tangent  AD  indefinite. 
Make  AD  equal  AD,  Fig.  12.  Make  UJ' equal  AD  and  to  tan- 
gent the  bcmiciiele  at  F.  Draw  J^O  for  the  joint  on  plan,  then 
the  wreaih-pieee  will  cover  so  much  of  the  plan  that  lays  between 
A  and  the  joint  at  F.  From  F  to  E  will  be  level,  the  solid  lines 
bhows  the  pattern  for  the  same,  it  being  a  little  over  a  ((uarter  of 
a  circl".  raialiel  with  tangents  DA  and  DF  draw  FH  and  AH, 
From  i^and  at  right  angles  to  AD  prolonged  draw  FG,  draw  the 
diagonal  OD. 

Now  return  to  the  elevation  Fig.  12,  draw  JM  parallel  to  XX 
and  prolonged  to  the  left.     Make  ilfiV  equal  the  chord  A  J',  Fig. 


144  Plate  30. 

11.  Make  CK  equal  DG,  Fig  11,  make  CQ  equal  DH,  Fig.  11: 
also  make  CL  equal  DO  on  plau.  Fig.  11;  draw  MQ  prolonged, 
cutting  the  perpendicular  from  L  at  U.  Fjom  K  and  at  right 
angles  to  RC  draw  KP. 

Bevels.  The  dotted  line  2  4  is  drawn  parallel  to  and  at  any 
distance  from  the  edge  of  l)oard  XX\  draw  2  5  perpendicular  to  XJS. 
and  equal  to  GF,  Fig.  11.  Make  2  3  equal  KP,  also  make  2  4 
equal  the  height  MC,  draw  5  3  and  5  4  to  edge  of  board  and  the 
angles  at  3  and  4  give  the  bevels  required.  Parallel  with  2  4 
draw  the  half  width  of  rail,  cutting  the  hypotheuuse  of  bevels  at 
7  and  8. 

Fig.  13.     Shows  the  face-would. 

Make  DA  e(iual  JC,  Fig.  12;  with  A  for  a  center,  and  the 
distance  NC,  Fig.  12.  as  a  radius,  draw  arc  at  P;  again,  with  D 
as  a  center,  and  DP,  Fig.  11,  for  a  radius,  draw  arc  intersecting 
at  F;  join  DP;  parallel  witli  DA  and  DP,  draw  PH  and  AH 
for  the  parallelogram  HADP  on  the  cutiiug  plane,  that  will 
agree  when  in  position,  with  the  parallelogram  HADP  on  plan. 
Fig.  U. 

Proof.     The  diagonal  DH  must  equal  the  distance  MQ,  Fig. 

12.  Prolong  DA  (V  to  J  for  length  of  shank;  make  joint  at  J" at 
right  angles  to  JD;  make  joint  at  F  perpendicular  to  DF;  pro- 
long joint  at  P  indefinite;  draw  the  diagonal  DH  io  intersect  the 
joint  line  from  F  at  O;  draw  OA  prolonged  for  the  trapezium 
OADF  on  the  cutting  plane,  that  will  coincide  with  the  trape- 
zium OADP  on  plan.  Fig.  11;  proof:  the  diagonal  DO  must  equal 
the  distance  MU,  Fig.  12,  if  so,  the  quodrilateral  is  correct. 

Draw  DC  perpendicular  to  OP;  make  OC  equal  the  radius 
OA,  Fig,  11:  then  O  is  the  center  to  pivot  the  trammel,  and  OP 
is  the  semi-major  axis,  and  OA  the  semi-minor  axis.  Make  J^  2 
and  J?'3  each  equal  4  8,  Fig.  12;  make  J  6  and  J  1  each  equal  3 
7,  Fig.  12:  draw  6  4  and  6  5  parallel  with  AJ;  make  C8  and  Ctf 
each  equal  the  half  width  of  rail  \^2,W]. 

Now  pivot  the  trammel  at  O,  with  the  arms  at  right  angles  to 
the  minor  axis  OC  then  set  from  pencil  to  minor  pin  the  distance 
O  8,  and  from  pencil  to  major  pin  the  distance  O  2;  now  trace  the 
curve  from  2  to  4  for  the  concave  side  of  mould;  proceed  in  like 
manner  to  trace  the  convex  and  center  line  of  mould.  At  section 
B  the  bevel  shown  in  the  angle  at  3,  Fig.  12,  is  applied  from  the 
face  of  crook;  at  section  iVthe  bevel  shown  in  the  angle  at  4,  is 
applied  from  the  face  of  crook.  Observe  the  bevels  do  not  cross 
the  tangents  in  their  application,  because  the  minor  axis  is  not 
within  the  parallelogram,  as  shown. 

Fig.  14.  Shows  how  to  ylacc  the  risers  in  the  cylinder 
m  as  to  hai'e  the  rail  the  T)ropcr  hei/jht  at  the  landing,  and 
make  the  torcath-piece  ivithout  nviy  spring  or  Joint  bevel  at  the 
shank;  thus  canting  the  plnnk  only  one  way. 

This  gives  the  most  simple  method  to  construct  the  face- 
mould;  the  rise  is  S^\  and  tread  9'^  the  elevation  is  first  drawn, 
then  the  plan.  ' 

liCt  XX  indicate  the  edge  of  drawing  board;  draw  BP  at 
right  angles  to  XX;  any  where  on  the  line  BP,  place  the  rise  of 
pitchboard,  and  draw  the  inclination  CJ" indefinite  for  the  center 
of  rail.  Parallel  with  CJ" draw  the  underside  of  rail;  at  C,  draw 
a  section  of  rail,frora  the  under  side  of  rail  section,  measure  down 
half  a  rise  [4'''']  to  the  floor  line  V;  draw  the  floor  line  parallel  to 
XX,  cutting  the  under  side  of  rail  at  O,  then  O  is  the  center  of 
short  baluster,  and  the  baluaters  are  2'^X2'^  then  the  face  of  No. 


Plate  30.  145 

IG  rise  will  be  V^  totho  left  of  O,  and  No.  15  rise  will  be  ^"  to 
the  left  of  that  again.  Now  cletermiue  the  radius  for  the  cylinder 
say  6*",  then  the  radius  for  the  center  line  of  rail  will  equal  6%''''. 
Make  JBA  equal  ^",i"\  perpendicular  to  XX,  draw  AE,  cuttinK 
JC  at  H;  draw  HM  prolonged,  and  parallel  to  XX;  draw  CK 
parallel  to  XX,  and  of  indefinite  length  for  the  direction  of  level 
rail. 

Fig.  15.    Shows  the  plan. 

Draw  the  two  right  angles  A  OC  and  CO^  indefinite;  make 
OC  e(iual  AB,  Fig.  14;  with  OC  [6%^^]  as  a  radius,  draw  the 
semi-circle  ACS;  draw  the  tangents  AB,  BC,  CD  and  DE. 
Prolong  tangent  BA  and  DE  to  the  left  for  the  direction  of 
straight  rail;  place  the  face  of  No.  15  and  16  rise  to  agree  with 
J  isers  in  elevation,  relative  to  the  spring  of  cylinder;  the  face  of 
No.  15  rise  is  located  7}^^^  from  the  diameter,  then  the  face  of 
No.  16  rise  will  be  in  the  cylinder  IJa^''. 

Keturn  to  Fig.  14,  make  HG  ecpial  the  chord  AC,  Fig.  1.5: 
parallel  with  BF,  draw  the  half  width  of  rail  [2 3^^'].  cutting  ffC 
at  3;  tlie  dotted  line  shows  the  thickness  of  plank  [4'^]  required 
for  the  wreath-piece. 

Fig.  16.  Shoivs  the  face-mould,  and  is  drawn  in  the  same 
manner  as  at  Fig.  5  and  10.  Observe  at  sections  N  and  D  the 
block  pattern  is  applied  at  the  center  of  plank  in  this  case;  the 
bevel  for  section  N  is  found  in  the  angle  at  C,  Fig.  14;  there 
being  no  spring  in  this  case,  the  try  square  is  applied  at  the  shank 
joint  section  D. 

Figs.  17  and  18.  Shows  the  same  principal  as  at  Fig.  14 
and  15  applied  to  a  platform  twist,  the  manner  to  find  the  location 
of  risers  in  the  cylinder,  and  the  construction  of  face-mould 
repeats,  and  in  this  case  is  the  same  as  shown  at  Fig.  16,  the  let- 
tering being  the  same. 

Let  it  lie  noticed  tlio  face  of  No.  15  rise  is  T'/j"  from  the  spring-  of 
cyliiidor  and  the  face  of  No.  IS  rise- is  0'^"  from  the  spring  line,  the 
difF«>rence  being  eaual  tohalf  tlie  thickness  of  balustei-.  This  method 
allows  in  this  case  two  more  balusters  (4)  to  he  placed  in  tlie  cylinder 
on  the  platform.  Also  observe  at  section  N,  Fi.s,^  1(5,  that  if  the 
wrey.th-piece  were  turned  upside  down  it  would  suit  for  the  wreath- 
piece  starting  off  the  platform. 

This  melliod  of  placing  the  risers  in  the  cylinder  makes  the  con- 
struction of  face-mould  and  formation  of  the  wreath  an  easy  matter. 
One  fault  is  in  a  "level  to  rake,"  and  "rake  to  a  level"  twist,  the 
joining  of  the  wreath-piece  with  the  level  auarter  turn  at  the  center 
join  t  in  small  cylinders  does  not  please  the  eye  so  well  as  wheu  both  the 
raking  and  level  wreath  pieces  are  sprung  at  the  shanks,  then  the 
"helix  "  or  twist  line,  in  passing  from  V  to  E,  Fig.  15,  gradually  lowers 
into  the  straight  part  of  rail  resulting  in  a  graceful  curve  pleasing  to 
the  eye.  Of  course  by  using  a  spring  bevel  more  work  is  required,  and 
in  cheap  work  the  easiest  method  is  mostly  resorted  to.  The  objective 
feature  referred  to  above  may  bo  remedied  by  cutting  thelevel  crook 
from  stuff  halt  an  incli  thicker  than  the  rail,  and  raising  the  (wist 
strip  so  as  to  c:u-ry  the  curve  gradually  from  the  rake  to  the  level, 
and  taking  tlie  surplus  wood  off  at  the  top  at  the  center  jouit,  and  off 
from  the  undeiside  at  shank  for  the  landing  twist,  and  for  thelevel 
part  of  twist  starting  the  block  jjattern  is  applied  so  as  to  take  the 
surplus  wood  from  the  underside  at  the  center  joint,  and  froTn  the 
upper  side  at  the  shank  as  shown  at  Figs.  22  and  23.  This  would 
increase  the  length  of  balusters  V^"  at  each  turn,  but  may  be  counter- 
acted by  raising-  or  lowering  the  block  pattern  at  the  shank  of  the 
raking  wreath  piece,  as  shown  at  section  JD,  Fig.  10.  As  the  center 
joint  is  plumb  this  treatment  of  the  above  wreath-pieces  makes  the 
center  joint  a  splice  joint  and  thereby  detracts  from  its  appearance 
to  some  e.xtcut. 


1^6  Plate  30. 

Pig.  19.  Shows  the  plan  of  a  12"  cylinder  for  a  platform 
stairs  having  two  different  pitcJies;  the  rise  to  the  platform  is 
8"X^"  tread,  and  off  the  platform  the  rise  is  6"y(J2"  tread; 
this  of  lea  happens  i7i  a  stairs  goiny  to  the  attic,  where  thefliglit 
off  ihc  platform  has  to  he  constructed  to  give  head  room  at  the 
landing  under  the  rafters. 

The  method  here  shown  is  to  construct  the  face-mould  so 
that  one  pattern  and  one  sit  of  bevels  will  answer  for  both 
wreath- in  c  CCS.* 

AB,  BC,  CD  and  DE  are  the  tangents  for  the  center  of 
rail  on  plan;  the  face  of  No.  S  rise  is  ^",  and  the  face  of  No.  11  rise 
is  lli"  from  the  joint  or  spring  of  cylinder;  No.  9  and  10  rise  is 
iu  the  cylinder. 

Pig.  20.  Shows  tlie  elevation  of  tangents,  they  being 
folded. 

Let  XX  represent  the  edge  of  drawing  board;  make  AB 
equal  AB,  Fig.  19;  perpendicular  to  XX,  draw  AE  and  BD; 
elevate  Nos.  8,  9,  10  and  11  rise  and  treada,  keeping  the  face  of 
No.  8  rise  b",  and  No,  11  rise  7}4"  from  the  spring  line  AEj  as 
shown. 

Through  the  center  of  balusters  00,00,  draw  the  inclination 
of  the  under  side  of  rail  for  both  inclinations;  parallel  with  00, 
OO,  draw  the  center  of  rail,  intersecting  at  F;  bisect  the  two 
pitches  at  G,  and  draw  GF  indetinite,  cutting  AE  and  BD  at  C 
and  H;  perpendicular  to  GF,  and  through  fi"and  C.  draw  JHP 
and  LCM,  cutting  the  center  of  rail  FN  at  i-*and  Q.  Perpen- 
dicular to  LM.  draw  QR:  join  CR  and  produced.  At  right 
angles  to  JP,  draw  PTe(iual  to  the  chord  AC,  Fitr,  19;  from  C. 
and  at  right  angles  to  FN.  draw  C  2;  again,  from  P,  and  perpen-- 
dicular  to  CR  produced,  draw  PZ;  parallel  with  ML,  draw  the 
half  width  of  rail,  cutting  CR  and  QP  at  4  and  5  for  the 
increased  width  of  mould  on  the  radial  lines. 

Bevels.  The  dotted  line  Z7 Vindicates  a  gauge  line  run  on 
parallel  to  edge  of  board  XX;  draw  UW  jx-rpendicular  to  XX, 
and  equal  to  HC,  Fig.  20;  make  Z70  equal  C2,  and  Ul  equal  JP 
3;  draw  W6  and  W7  prolonged  to  edge  of  board.  Then  in  the 
angle  TJQ'W,  is  found  the  bevel  for  the  shank  joint,  and  the 
angle  Z77W  gives  the  bevel  for  the  center  joint. 

Pig.  21.     Shows  the  face  mould. 

At  any  convenient  place  on  the  pattern  pai)erdraw  SJ"  indef- 
inite, make  BA  and  AJeach  eciual  QP  and  PN,  Fig.  30.  Then 
with  A  as  a  center  and  TH,  Fig.  20,  for  a  radius,  draw  arc  at  C. 
Again  with  B  as  a  cent(  r  and  RC,  Fig.  20,  as  a  radius,  draw  arc 
intersecting  at  C,  join  BC.  I'arallel  with  the  tangents  AS  and 
BC  draw  CO  and  AO  prolonged  at  A  and  C for  the  parallelo- 
gram OACB  on  the  catling  plane.  ISIake  AD  equal  QF,  Fig- 
20.  .Toin  DO  and  piolonged  for  the  direction  of  the  minor  axis, 
then  at  right  angles  to  DO  and  through  O  draw  the  direction  of 
the  major  axis  EF. 

Make  O  2  e<iual  HC,  Fig.  20,  let  2  3  and  2  4  each  equal  the 
half  width  of  rail.     Make  C5  and  C  6  each  equal  Q  5,  Fig.  20. 

S^"  *This  inelhod  of  solving  this  problem  in  hnnd-railinjf,  first  ap- 
peared in  "Ciapaitrjj  and  Building,"  for  Julj',  1H84,  A'ol.  (5,  Pajre  146. 
This  joiirnnl  is  published  in  New  York,  by  David  Williams,  and 
slionld  beslndiod  and  proscrvod  liy  every  carpenter  in  tlie  country; 
by  having  ihe  nurnlx-rs  bound,  llicy  serve  as  a  ready  reference  and 
encyclopaedia  on  all  that.  ai)pcrtains  to  the  trade;  especially  to  the 
young  man  it  is  a  valuable,  practical  instructor. 


Plate  31.  147 

Let  A  7  and  A  8  each  equal  C  4,  Fig.  20,  draw  8  10  and  7  9 
parallel  with  AJ.  Make  joint  at  j  at  right  angles  to  the  tangent 
J'B  and  the  joint  at  C  make  perpendicular  to  the  tangent  BC 

Now  pivot  the  trammel  at  O  and  trace  the  curves  for  the  inside, 
outside  and  center  line  of  the  face-mould  as  explained  at  former 
plates. 

The  application  of  the  bevels  is  shown  at  sections  F  and 
N.  For  the  points  on  the  pattern,  to  cut  the  straight  rail,  make 
JM  equal  iVS,  Fig.  20,  fur  the  length  to  the  platform,  and  for  the 
length  of  the  platform  make  JL  equal  3r9,  Fig.  20.  Now  meas- 
ure from  these  two  points  JWaud  i  instead  of  the  point  A,  as  in 
other  cases. 

It  will  be  observed  that  in  drawing  the  face-mould  in  this  way  so 
as  to  make  one  pattern  and  one  set  of  tievels  answer  for  the  two  dif- 
ferent inclinations,  the  twist  when  blocked  out  will  not  be  plumb 
at  the  center  joint.  This  will  not  he  noticed  much  for  a  small  flat 
rail,  but  for  a  high  double  rail  the  sides  will  show.  This  can  be 
remedied  some  liy  working  the  wreath  a  little  full  at  the  center 
joint  and  dressing  olf  agreeable  to  the  eye,  after  the  two  wreath 
pieces  are  bolted  together. 

Figs.  22  and  23.  Show  two  quarter  turns  to  connect  a 
stiirtinrj  and  landing  twist.  Tlie  tamjcnts  agree  with  those  on 
plan. 

The  explanation  for  Fig.  4,  Plate  16,  will  apply  iu  this  case 
aiul  needs  no  other  explanation  further  than  to  say  better  results 
will  follow  by  springing  the  plank  for  both  wreath-pieces,  similar 
to  Fig.  4,  plate  16,  but  will  take  more  time. 


PLATE  31. 


Plate  31.  [Scale  }{^^=^l  foot].  Exliibits  plan  a)ui  eleva- 
tion of  a  one-story  platform  staircase. 

The  height  of  story  from  top  to  toj)  of  joist  equals  12^  H'^. 
width  of  joist  in  the  second  story  is  10^^,  width  of  hall  10' 3^'' 
iu  the  rough;  run  of  first  flight  including  the  platfonn  IS'  0'^; 
the  door  under  the  i)latform  is  7'  6''  high;  steps  are  1^^^  thick, 
rail  SM''  l)y  5/^  double  moulded;  balusters  2'^  by  2''';  newel  post 
10'^  by  10-",  and  a  left  handrail. 

Fig.  1.  Shows  the  2)lan.  Having  sixteen  risers  to  the  plat- 
form in  the  first  flight  and  five  risers  in  the  return  flight  to  the 
lauding  in  the  second  story,  making  twenty-one  risers  iu  the  height 
of  story.  The  cylinder  is  24 '^  in  diameter  and  the  steps  are 
spaced  off  on  the  cylinder  line  equal  to  the  regular  tread.  The 
center  of  newel  is  placed  in  the  center  of  hall.  The  three  first 
treads  at  the  wall  string  are  increased  gradually  in  width  lOVg'''', 
llli'^  and  IS^a",  while  at  the  front  string  they  are  equal  to  the 
regular  tread  iu  width,  allowing  a  gradual  "swell  "  on  the  nosing 
line. 

Fig.  2.  Shores  the  elevation. 
The  height  of  story  12'  y"  is  divided  off  on  the  story  rod  AB, 
into  21  risers,  thus  12'  o"  reduced  to  inches  (10'3"X12'''~147") 
equals  147",  which  divided  into  21  divisions  (147"-h21=:-7"), 
etiuals  7"  for  the  height  of  each  rise.  If  we  use  the  constant 
of  21"  (24"— 7"-;  7"- 10")  as  before  we  will  have  10"  for  the 
width  of  the  regular  tread.  Now  there  are  16  risers  to  the  plat- 
form at  7"  each  (16''X'<"'^11~''^-^13'':=9'  4"),  equals  9'  4"  for 
the  height  of  platform.     The  height  of  door  under  the  platform 


148  Plate  31. 

is  specified  to  be  1'  6^^  tlien  9^  ^"  minus  7^  <^"  equals  V  W^ 
for  the  space  from  top  of  door  to  top  of  platform.  The  depth 
of  joist  is  10  and  thickness  of  floor  is  \"  and  plaster  \" 
(10'^+1^^+1^^=12^0  equals  twelve  inches,  leaving  W.  That 
amount  is  ample  for  the  linish  over  the  door. 

Tin;  ru!!,  including  the  platform,  is  reciuired  to  be  18''  Q" , 
there  being  12  treads  in  the  first  flight  at  W^  each  [12X10=' -0| 
plus  tliree  odd  treads  that  are  10K^^  113-^^'  and  V.W-."  wide 
(120X10}^^^+llK'^-fl-:!K^'=155>.i^O  equals  15.5K  inches,  which 
reduced  to  feet  (155K''^-^12=:12'  11>2^0  equals  12^  ll>a'^  for 
the  horizontal  run  of  the  treads  to  tlie  platform.  Then  the  width 
of  platform  to  the  face  of  No.  16  ri.se  will  equal  IS''  ^"  minus 
12^  \\)4,"  (18'  ^"—W  ny/^=5^  oy/')  or  5'  OK'''  as  sliowu  on 
plan. 

Again,  the  thickness  of  rise  equals  V^  and  allow  13^''  for 
uneven  walls,  the  platform  may  be  framed  4''  IC  (o'  oy^^ — 1''^4- 
iy^^=2}4'^)=i'  lO'O  for  the  neat  width. 

The  flight  off  the  platforni  has  5  risers  and  4  full  treads  at 
10'''  each,  then  there  should  be  6"  from  the  last  rise  to  the  face  of 
joist  at  the  landiug,  so  that  the  bearers  may  have  good  nailing 
against  the  joist.  The  width  of  platform  from  the  face  of  No.  l(j 
rise  to  wall  equals  5'  03<".  the  distance  then  from  the  wall  to  face 
of  joist  at  the  landing  A,  (4X10"+5'  0>.i"=8'  10>i'O  equals 
8''  ioy,  as  shown  on  plan. 

Headway.  For  the  headway  count  down  from  the  landing, 
s;iy  16  risers  at  7'-'  each  minus  the  width  of  joist  10'''  in  the  secoiul 
story,  thickness  of  floor  1"  and  1"  for  the  plastering  (1  OX'' ^^= 
113)— 10"+1"J-1":^100"-T-12"=8'  4")  equals  8'  4"  plumb 
over  and  includin,'  No.  6  rise.  In  this  case  No.  6  rise  should 
be  deducted  from  b'  4",  leaving  7' 9"  for  the  head-room.  So  we 
will  locate  the  face  of  trimmer  plumb  over  the  center  of  No.  5 
step.     This  will  give  ample  head-room. 

Thoi  from  the  back  of  platform  to  the  face  of  trimmer  marked 
Cfatthe  headway  will  equal  5'  03^"  from  the  back  of  platform 
to  the  face  of  No.  16  rise  plus  10  treads  at  10"  each  .5'  OK'^  + 
(10X10"=100")^12  =8'  4"+.5"+5'  03^"=13'  9M")  equals  13' 
93^".)  And  the  length  of  quarter  pace  landing  marked  AJSon  i)lau 
will  equal  13'  934"  minus  8'  103^"  U3'  93-^"— 8'  10>^"=4'  11"), 
or  4'  11"  for  the  length  of  trnnming  at  the  landing,  and  the  width 
08  qiuirter  puce  will  e  lual  the  width  of  hall  (10'  3")  minus  the 
half  width  of  hall  (."/  13<")  plus  the  radius  of  silver  12"  and 
the  thickness  of  fascia  (132^0  «r  outer  string  (10' 3"— [.5'  13'.<"^- 
vy'-\-i)4'^=-P,^  ^A'  0")  equals  4'  0"  for  the  width  of  landingfrom 
thorough  wall  to  the  face  of  header  marked  C,  on  plan.  Fig.  1. 
This  completes  the  trimming  for  the  well  of  staircase. 

Tho  joist  at  the  landing  should  be  well  bridged  and  spiked  to 
prevent  sagging;  if  the  walls  are  brick,  the  platform  should  be 
framed  and  l)uilt  in  when  the  vi'alls  are  going  iq),  by  leaving  a 
space  over  each  joist,  the  i)latform  may  be  levciled  u])  when  put- 
ting up  the  stairs.  At  the  terminus  of  the  lail,  a  block  should  bo 
built  ill  the  wall  ?/  8"  from  the  floor  to  its  center,  for  to  fasten 
the  rosette  and  rail;  if  stud  partitions,  see  that  the  block  is  set  far 
enough  back  for  the  plastering  to  key. 

At  h,  h,  are  .shov/n  the  rough  brackets  underneath  the  stairs 
cut  and  nailed  to  3''V4"  bearers,  liaving  the  grain  i)erpendicular 
to  the  treads.  At  H  is  .shown  the  panel  work  under  the  lirst 
flight,  having  an  arched  opening  into  a  coat  closet  or  wash-stand; 
tho  bize  and  variety  of  panels  may  bo  arranged  to  suit  the  taste  of 
architect  or  stair-builder. 


PrATR  SI,  149 

Eig.  3.  [Scale  X''=\  foot].  Shows  the  plan  of  cylinder 
24^^  in  diameter. 

The  risers  Nos.  15,  16, 17  and  18  are  spaced  off  on  the  stretch- 
out AD,  and  are  drawn  into  the  cylinder  at  L  and  N  to  suit  the 
lx)sition  of  balusters  in  the  same  manner  as  explained  at  Plate  15, 
which  should  be  well  studied. 

From  D,  on  the  stretchout,  to  F,  equals  half  a  tread  (r/'), 
and  is  tlie  face  of  No.  10  rise;  and  fronx  F  to  K,  and  K  to  G, 
each  equal  to  a  full  tread  (IC),  and  are  the  face  of  Xo.  14  and 
15  risers,  thus  establishing  the  face  of  No.  14  rise  6^^  from  the 
spring  line  AC,  as  shown. 

Draw  No.  17,  IS  and  19  rise  opposite  to  No.  Ifl,  15  and  14 
rise,  and  locate  the  short  balusters  on  No.  14  and  V.i  treads;  then 
space  off  the  intervening  balusters  equally,  and  curve  the  face  of 
risers  No.  16  and  17  to  suit  the  balusters  as  shown. 

The  outer  solid  line  ABC  shows  the  face  of  cylinder;  the 
outer  dotted  line,  indicates  the  center  line  of  rail  3*i'^  from  the 
cylinder  line;  the  inner  dotted  line  shows  the  thickness  of  braclcet 
{^i'^),  and  the  inner  solid  line  1,  2,  3,  4,  shows  the  projection  o/' 
nosing,  (IK^O- 

Fig.  4.  Shown  the  semi-rirclc  ABC,  divided  off  into  an  odd 
number  of  staves  (11);  the  chord  or  tlie  segment  for  No.  1  stave 
is  extended  to  the  edge  DE,  of  drawing  board;  for  a  convenient 
means  to  adjust  the  bevel  F,  a  greater  or  less  number  of  staves 
may  be  used,  as  the  stair-builder  may  desire;  this  ^vi^lth  of  staves 
answers  very  well  for  the  'treads,  and  is  intended  to  be  made 
from  stuff  IK^^  thick.  At  Fig.  1,  Plate  33,  is  shown  how  to 
obtain  the  length  of  staves. 

Figs.  5  and  6.  [Scale  1}4^'^V\.  Shows  the  convex  and 
concave  risers. 

The  end  of  risers  are  slit,  forming  a  veneer  CC,  about  ^/^ 
thick,  steamed,  bent,  glued  and  clamped  to  the  cores  A  and  B, 
for  the  proper  curve;  "cauls"  are  clamped  down  over  the  veneer 
to  press  them  close  and  even  to  the  core. 

Fig.  7.  Shoivs  plan  of  the  turnout  at  the  neivel,  divided 
into  three  staves,  and  spliced  to  the  outer  string;  then  screwed 
from  the  back. 

The  face  of  No.  4  rise  is  5^^  from  the  spring  of  cylinder,  the 
radius  is  2^  Wi'^  and  should  be  drawn  on  heavy  paper,  as  shown  at 
Fig.  9,  Plate  32.  The  bevel  for  jointing  the  staves  is  shown 
at  A. 

The  cut-out  for  No.  14  rise  is  ^%"  from  the  joint  of  cylinder; 
at  No.  19  rise  the  cut-out  of  outer  string  is  Q\i'^  from  the  joint  of 
cylinder;  the  width  of  string  at  the  internal  angle  of  thread  and 
rise  is  6^''.  The  jointing  of  the  staves,  glueing  and  splicing  to  the 
strings  has  been  described  under  a  1^'  cylinder.  Also  preparing 
the  steps  and  stepping  up  is  the  same  as  has  been  explained  for  a 
7^^  and  13^^  cylinder,  at  Plates  23  and  35. 

Measuring  for  jointing  the  rail  at  the  bench.    The 

first  length  [11'  6''^],  for  jointing  the  rail,  is  shown  taken  from 
spring  of  turnout  to  the  spring  of  cylinder;  the  second  length 
[3''  8''J  is  taken  from  the  spring  of  cylinder  to  the  face  of  last 
rise  landing;  the  third  length  [4'  ^y/']  is  taken  from  the  face  of 
last  rise  landing  to  the  spring  of  quarter  cylinder;  and  the  fourth 
and  last  length  [5'  IK^^]  is  taken  from  the  spring  of  quarter  cyl- 
inder to  wall.  All  these  lengths,  and  also  the  dimensions  of 
pitch-board  [7''X10^^]i  should  be  entered  in  the  order  hook.' 


is^  Pr.ATE  32. 


PLATE  32. 

Plate  32.  [Scale  X^^=V].  ExMUts  the  construction  of 
face-moulds  for  a  stair-ease,  Plate  31. 

Fig.  1.  Shows  the  plan  of  the  center  line  of  rail,  and  the 
tangents  for  the  same. 

Draw  the  diameter  line  AE,  and  the  radius  OC,  indefiuito, 
and  at  right  angles  to  each  other;  then  witli  12yi^^  for  a  radius, 
and  O  as  a  center,  draw  the  semi-circle  ACE,  for  the  center  of 
rail;  the  dotted  line  shows  the  face  of  cylinder  or  outer  string 
line. 

Enclose  the  semi-circle  with  the  rectilineal  parallelogram  to 
tangent  the  semi-circle  at  the  points  A,  C  and  E,  and  we  have 
the  two  square  parallelograms  OABC  and  OCDE.  on  plan. 
Prolong  tangents  BA  and  DE,  to  the  right  for  the  direction  of 
straight  rail.  The  position  of  risers  in  the  semi-circle  are  the 
same  as  at  Fig.  3.  Plate  31;  the  face  of  No.  14  and  19  rise  is  iV^ 
from  the  spring  of  cylinder.  The  balusters  No.  1,  2,  3,  &c,,  are 
spaced  olf  on  the  center  line  of  rail  and  drawn  normal  to  the 
curve  at  their  centers. 

Fig.  2.  Shows  the  elevation  of  tangents;  they  are  nn 
folded. 

Let  XX  indicate  the  edge  of  drawing  board,  Make  AJB* 
BC,  CD  and  DE,  each  equal  AB,  BC,  CD  ainl  DE  on  j.lan, 
Fig.  1.  Perpendicular  to  XX,  draw  AF,  BG,  CH,  DJ  and 
i7ir  indefinite.  Now  elevate  Nos.  1.",  14,  15,  Ki,  17,  18.  19  and  20 
risers  and  treads,  keeping  the  face  of  No.  14  and  19  rise  6^^  from 
the  spring  lines  AF  and  EK. 

Tlnoiigh  the  center  of  baluster  SOO,  on  the  riglit,  and  00,  on 
the  left,  draw  the  inclination  for  the  underside  of  rail;  parallel 
with  00,  draw  the  center  of  rail,  cutting  JE7ifand  JD  at  L  and 
M,  on  the  left.  And  on  the  right,  cutting  A^  and  JBG^,  at  JV 
and  P;  connect  PM,  cutting  CHat  Q.  At  right  angles  to  CH, 
draw  QR  and  LS,  cutting  DJ  at  T  and  U;  then  ML  is  tlie 
lieight  of  the  wreath-piece  for  the  (puirter  circle,  fiom  C  to  E,  on 
plan,  Fig.  1;  and  the  height  for  the  quarter  circle  from  A  to  C  is 
the  same  as  shown  at  NV.  Prolong  LM  to  intersect  RQ  at  W; 
also  prolong  QM  to  intersect  EK  at  Y. 

Make  LZ  equal  to  the  chord  AC,  Fig.  1;  at  M  set  off  the 
half  width  of  rail  on  each  side  of  DJ;  parallel  with  DJihuw  the 
half  width  of  rail,  cutting  the  tangent  MQ  at  3,  and  tlie  tangent 
LM  at  3.  From  T,  and  at  right  angles  to  LW,  draw  r4;  from 
U,  and  perpendicular  to  YQ,  draw  U  5. 

Bevels.  Let  6  6  indicate  the  edge  of  drawing  board,  and 
the  dotted  line  indicate  a  gauge  line  parallel  with  the  edge  of 
board.  Make  7  8  perpendicular  to  6  6,  and  equal  to  the  radius 
|12M^^J  OC,  Fig.  1.  Make  7  9  equal  to  T'4,  and  7  10  equal 
J75;  draw  8  9  and  8  10  prolonged  to  6  6;  the  angle  at  9  gives  the 
joint  bevel  for  the  sliauk,  and  the  angle  at  10  gives  the  bevel  for 
center  joint. 

Fig.  3.     Shouis  the  face-mould. 

At  any  convenient  place  on  the  pattern  paper  draw  JD  in- 
definite; make  DE  equal  LM,  Fig.  2;  let  EJ  equal  P/''  more  or 
less,  for  length  of  shank.  With  E  for  a  center,  and  the  distance 
jRZ,  Fig.  2,  as  a  radius,  draw  arc  at  C;  again,  with  JD  for  a  cen- 


Pt-ate  S2.  151 

ter,  and  the  tangent  MQ,  Fig.  2,  as  a  radius,  draw  arc  inter- 
secting at  C;  connect  DC  parallel  with  tangents  DE  and  DC; 
draw  CO  and  EO,  establishing  the  center  O  for  the  trammel,  and 
the  parallelogram  OEDCon  the  cutting  plane  that  will  agree  when 
in  position  with  the  parallelogram  OABC  on  plan  Fig.  1. 

Proof.  If  the  diagonal  OD  equals  the  distance  ZY,  Fig.  2, 
the  angle  at  D  must  be  correct. 

I'rolong  OE  and  OC.  Make  EF  equal  MW,  Fig,  3;  draw 
OF  produced,  through  O,  and  at  right  angles  to  OF,  draw  AB, 
for  the  direction  of  the  major  axis;  make  0  2  equal  OC,  Fig,  1, 
(12M'^).  Let  2  3  and  2  4  each  equal  the  half  width  of  rail 
(1%'^);  make  C5  and  C(%  each  equal  M  3,  Fig.  2.  Also  E  7 
and  i7  8,  each  equal  M  2,  Fig.  2.  Parallel  with  i^J",  draw  7  9, 
and  8  10;  make  joints  at  J"  and  C  perpendicular  to  the  tangents 
DJ  and  DC,  Now  pivot  the  trammel  at  O,  with  the  amis  cen- 
tered on  the  axis  line  AB;  then  set  from  pencil  to  minor  pin  the 
distance  0  2,  (12%^^),  place  the  pencil  at  C,  and  slide  the  major 
pin  until  both  pins  drop  into  the  grooves;  then  fasten  the  major 
pin,  and  trace  the  elliptic  curve  through  the  points  C2E,  for 
the  center  line  of  rail;  proceed  in  the  same  manner  to  trace  the 
concave  and  convex  curves  of  face-mould. 

At  section  M  and  N,  the  bevels  are  shown  applied  through 
the  center  of  plank;  the  shaded  part  shows  the  amount  of  over 
wootl  to  be  removed,  and  also  the  thickness  of  plank  required  for 
the  wreath-piece. 

Pig  4  Repeats  Fig.  3,  the  lettering  being  the  same,  and  indicates 
tlie  fiice-inould,  Fig.  3,  turned  over,  and  the  tangents  lined  off  on 
liie  oijposite  side;  the  figure  is  introduced  liere  to  show  the  learner 
liow  thu  bevels  are  applied,  so  as  to  mate  thuiu  for  a  platform  twist. 
(Jl)serve  at  N.  Fig.  3,  the  bevel  is  applied  so  as  to  pitch  the  shank  EJ, 
down;  and  at  section  N,  Fig.  4,  tlie  bevel  is  shown  applied  from  the 
face  of  i)lank,  and  the  i-everse  way,  so  as  to  pitch  the  shank  EJ,  up; 
and  al  the  sliank,  section  M  sliows  the  bevel  apijliod  so  as  to  piicli  the 
joint  at  C,  down;  and  at  Fig.  3,  section  M  shows  the  bevel  applied  .so 
as  to  pitch  the  joint  at  O,  up,  thus  mating  the  two  crooks.  Fig.  3 
forms  tlie  wreath-piece  landing  on  tlie  platfoi'is;  and  Fig.  4,  the 
M'roalh-piece  olf  the  platform.  The  learner,  bj'  trying  the  two  crooks 
together,  will  see  if  the  bevels  are  applied  correctly. 

Pig.  5.  Shows  the  elevation  of  the  two  irrcatJirjyicces ;  the 
iangoits  being  folded. 

]"ig.  2  sliows  the  tangents  unfolded;  it  will  be  obvious  to  the 
learner,  after  la  little  study,  that  for  a  platform  twist,  all  the  lines 
lUM^essary  to  obtain  the  face-mould  may  be  found  in  tliis  way,  with- 
out the  trou1)le  of  unfolding  all  the  tangents.  See  Fig.  2  Plate  29; 
also,  Figs.  9  and  11,  Plate  33;  unless  it  be  required  to  find  the  lengths 
of  odd  baluster.s;  then  the  development  of  tangents  together  with 
the  treads  and  risers  becomes  necessary. 

How  to  obtain  the  length  of  odd  balusters.  Re- 
turn to  Fig.  1;  prolong  tangents  AB  and  i7Z)  to  the  left;  make 
BF  and  DG,  each  equal  WT,  Fig.  2.  Connect  FC  and  GC, 
lor  the  directors;  from  the  center  of  b'llusters  2,  3,  4,  draw  lines 
parallel  to  CF,  intersecting  the  tangeniS  AB  and  BC,  at  9,  10 
and  11.  Also  from  the  center  of  balusters  6,  7  and  8,  draw  lines 
parallel  to  the  director  GC,  intersecting  the  tangents  at  the 
points  12,  13  and  14,  as  shown. 

Now  we  have  the  position  of  balusters  on  the  tangents  on 
plan,  relative  to  their  position  on  the  tangents,  on  the  cutting 
plane. 

Keturn  to  elevation.  Fig.  2,  and  transfer  the  location  of  each 
baluster  from  the  tangents  on  plan.  Fig.  1,  to  corresponding  posi- 
tion in  elevation,  Fig.  2,  as  shown  at  9,  10,  11.  12,  &c.  Setoff 
the  under  side  of  rail  parallel  to  the  line  of  tangents;  draw  the 
conlcr  of  baluster  perpendicular  to  the  treads,  to  intersect  the 
under  side  of  rail,  as  9  2,  10  3,  11  4,  12  5,  &c. 


\n2  I'l.ATE   Sa. 

Now  as  the  under  side  of  rail  is  drawn  through  the  center  of 
the  regular  short  balusters  at  00,  and  the  length  of  a  regular 
short  baluster  is  2'  V  from  the  top  of  step  to  the  under  side  of 
rail  measured  at  its  center;  then  the  baluster  marked  No.  9,  will 
be  li'^  longer  than  a  n-gular  short  one;  anil  the  baluster  marked 
No.  10,  will  equal  4>ft''^  longer;  and  No.  11  baluster  will  equal 
13^^'' longer;  No.  12  will  be  zy/^  longer;  No.  13  will  equal  y^ 
shorter;  No.  1-4  will  equal  \W  longer;  and  No.  1.5  baluster  will 
be  K'^  shorter  than  a  regular  short  baluster,  ?J  0%^',  from  the 
top  of  No.  18  step  to  the  under  side  of  rail  at  the  center  of  bal- 
uster, and  a  regular  long  baluster  will  be  half  a  rise  or  SJ^'''' 
longer  than  a  regular  short  one.  The  length  of  short  baluster  is 
taken  for  the  standard  because  the  under  side  of  rail  is  drawn 
through  the  center  of  balusters  00  and  00:  and  the  length  of 
balusters  at  those  points  is  naught,  as  shown  in  elevation.* 

Figs.  6,  7  and  8.  Shmo  the  jAan,  elevation  and  face- 
mould /(^r  Vie  Uirnont. 

Pig.  6.     Shows  the  plan. 

Let  D  indicate  the  center  of  newel,  set  off  13^'  to  the  face  of 
outer  string,  and  %^^  more  to  the  center  of  rail  at  L.  Draw  LA 
indefinite.  If  the  post  be  a  pedestal  newel,  set  the  same  to  show 
the  two  sides  to  the  best  advantage;  draw  DB  at  right  angles  to 
the  side  of  newel;  make  the  end  of  wreath-piece  at  C  to  enter 
the  newel  }4^^'  Make  BA  equal  BC,  locating  the  point  A  in 
this  case  5''  from  the  face  of  No.  4  rise. 

From  A  and  C,  draw  lines  perpendicular  to  AB  and  BC, 
converging  at  0;  then  with  O  for  a  center,  and  OA  as  a  radius, 
draw  the  center  line  of  rail  from  A  to  C;  then  AB  and  BC  will 
be  tangent  to  the  curve  at  the  points  A  and  C,  The  dotted  line 
at  A  shows  the  face  of  outer  string,  and  makes  the  radius  %''-' 
less  for  the  curve  of  cylinder  or  2^  IM^^-  Locate  the  short  bal- 
uster on  No.  4  step,  and  space  off  the  intermediate  balusters  to- 
wards the  newel. 

Now  curve  the  risers  to  suit  the  spacing  of  balusters  and 
position  of  newel;  parallel  with  the  tangents  BA  and  BC,  draw 
A  J*  and  CP  for  the  parallelogram  PCBA  on  plan;  from  C,  and 
perpendicular  to  AB  prolonged,  draw  CL. 

Pig.  7.  Shows  the  elevation  of  tangents,  they  are  folded; 
also  the  treads  and  risers. 

Let  XX  indicate  the  edge  of  drawing  board.  Make  AB 
equal  AB  on  plan  Fig.  6,  perpendicular  to  XX,  draw  AR  and 
BD  indefinite;  now  elevate  Nos.  1,  2,  3  and  4  risers  and  treads, 
being  careful  to  keep  the  face  of  No.  4  rise  5^^  from  tlie  spring 
AR. 

From  the  top  of  No.  1  step  set  up  6^''  to  the  underside  of  rail 
andSK^''  additional,  plus  the  height  of  a  rise  {lo}4'^)  to  the  center 
of  rail  at  F,  making  153^''''  from  the  floor  line  to  the  center  of  rail. 
Then  the  height  of  newel  from  the  floor  line  to  the  center  of  rail 
will  equal  \b}i''  plus  the  length  of  a  short  baluster  (9/  V),  or 
(1'  3K''+2'  l'^=3^  ^H^^)  equal  to  3^  4K''^ 

•' *The  standard  lengths  for  balusters,  as  furnished  to  the  market, 
are  cut  2'  4"  to  2'  0"  for  short  ones,  iiad  2'  8"  to  2'  10"  for  loii^  Ijsilusters, 
ill  proportion  of  one  short  baluster  to  three  \on%  ones;  tlie  standard 
leiig-tli  for  solid  newels  is  4'  0",  or  cut  in  scantlinaj  len^iths  of  8',  ICK, 
12'  and  16'.  and  in  squai-es  of  5s,  6s,  7s,  8s  and  10s;  for  angle  newel.s, 
the  lengths  run  from  5'  ti"  to  6'  0"  long.  Plank  for  stair-builders' 
use  Is  sawed  iVa",  2%",  :tH",  35g",  iVs",  i%",  SJg"  and  OJi"  in  thickness, 
f loni  forest  timber,  straight  in  the  grain,  and  free  from  shakes,  knots 
and  sap  wood. 


Plaie  32.  loo 

Draw  FE  parallel  to  XX,  cutting  BD  at  W;  through  th<« 
center  of  balusters  00  draw  the  under  side  of  rail;  parallel  to  00 
draw  the  incliuatiou  for  the  center  of  rail,  cutting  the  spring  and 
angle  lines  at  R  and  K,  and  also  cutting  i^^  at  J";  draw  JCJE7*. 
Make  EQ  equal  the  diagonal  BP,  Fig.  6;  make  EM  equal  the 
chord  ACon  plan  Fig.  fi;  let  i?iV equal  twice  if  W";  make  WP 
equal  BL,  Fig.  6,  from  P,  and  at  right  angles  to  GJ  prolongi  d 
draw  PH;  make  EL  equal  the  diagonal  BO,  Fig.  6;  draw  NQ 
prolonged  to  intersect  the  perpendicular  from  L  at  Z. 

As  the  radius  on  plan  in  this  case  is  2''  2^^  for  the  center  line 
of  rail,  it  will  require  a  large  trammel,  and  also  more  room  to 
draw  the  curves  of  mould;  therefore  we  will  find  points  in  the 
elliptic  curve,  from  the  chord  line,  through  which  to  trace  the 
curves  of  face-mould. 

Jteturn  to  plan  Fig.  6.  From  the  center  O  draw  the  half  width  of 
rail  equally  on  each  side  of  the  center  line  (l.?i^O-  Make  BJ 
equal  "WJ,  Fig.  7;  connect  cTCforthe  directing  ordinate;  draw 
(he  chord  AC;  bisect  AC  at  R;  bisect  JRCand  RA  at  Tand  S. 
From  the  points  A,  S,  R,  Tand  Cdrawordinates  parallel  to  JC, 
cutting  the  inside,  center  and  outside  of  rail  on  plan  at  the  points 
2,  :;  and  4;  fnnn  A,  and  at  right  angles  to  CJ  prolonged,  draw 
AK;  draw  CM  indefinite  and  at  right  angles  to  JC,  cutting  the 
curve  of  rail  on  plan  at  5  and  6. 

Bevels.  Return  to  elevation  Fig.  7;  let  YY  indicate  a  l)a?o 
line;  draw  2  2  parallel  to  YY;  draw  3  14  perpendicular  to  XX, 
and  equal  to  AK,  P'ig.  6.  Make  3  5  equal  to  CL.  Fig.  6:  make 
3  6  equal  HP;  also  make  3  7  equal  the  height  ER.  Draw  14  7 
and  5  G  prolonged.  The  angle  at  7  gives  the  bevel  for  the  joint 
connecting  the  newel,  and  the  angle  at  6  gives  the  bevel  for  the 
shank  joint.  Parallel  to  2  2,  draw  the  half  width  of  rail  {i%'^), 
cutting  the  hypothenuse  5  G  at  10;  also  make  2  9  and  2  15  each 
equal  (75  and  CG,  Fig.  G.  From  0  and  15,  and  parallel  to'  2  2, 
draw  9  12  and  15  16. 

Fig.  8.    Shou's  the  face-mould. 

Draw  GJ  indefinite;  make  RK  equal  RK,  Fig.  7;  with  R 
for  a  center  and  the  distance  RM,  Fitr.  7,  as  a  radius,  draw  arc  at 
C;  again,  with  K  for  a  center,  and  KE,  Fig.  7,  as  a  radius,  draw 
arc  intersecting  at  C;  draw  KC  prolomred.  Parallel  to  KR  and 
KC  draw  CO  and  RO  tor  the  parallelogram  OCKR  on  the  cut- 
ting plane. 

Proof.  The  diagonal  OK  must  equal  the  distance  QN,  Fig. 
7;  if  .so,  the  angle  of  tangents  at  K  is  correct. 

Make  KJ  equal  KJ.  Fig.  7;  join  JC  f<u'  the  director;  draw 
the  chord  RC;  bisect  RC  at  A;  bisect  AR  and  AC  at  /S  and  T; 
from  the  pi/ints  T,  A,  S  and  R  draw  ordiiiates  indefinite  and 
parallel  to  the  director  JC.  Now  transfer  the  points  2,  3,  4  on 
ordinates  on  plan  Fig.  6  to  coiTespondingordinates  on  face-mould, 
as  A.  2,  3,  4;  make  shank  RG  equal  6'^;  make  joint  at  G  at  right 
angles  to  tangent  GK;  make  joint  at  G  ))iMi)endicutar  to  the 
director  JC;  make  C5  and  CG  each  equal  7  12  and  7  16,  Fig.  7, 
respectively;  make  G"  and  GS  each  equal  G  10,  Fig.  7.  Pro- 
long the  diagonal  KO  to  equal  the  distance  NZ,  Fig.  7,  at  D; 
draw  DR  at  9  and  10  for  the  points  of  contact.  Now  trace  the 
curve  for  the  concave  side  of  mould  through  the  points  2,  2,  2,  &c.. 
and  through  the  points  4,  4,  4,  &c.,  for  the  convex  side,  using  a 
flexible  strip.  ^ 

'  *The  intention  here  is  to  show  liow  tlio  face-mould  may  be  drawn 
for  a  tui-nout,  when  both  tajigenta  are  inciiniug. 


154  Plate  33. 

The  section  at  N,  shows  the  bevel  found  iu  the  angle  at  6, 
Fig.  7;  the  block  pattern  determines  the  thickness  of  plank 
required;  the  section  at  B,  shows  the  rail  larger  than  the  regular 
size,  because  the  joint  5  6,  on  plan,  Fig.  6,  is  drawn  obliciue  to 
the  curve  of  rail  on  plan,  thus  increasing  the  section  of  rail  on 
the  joint;  if  the  joint  was  made  on  the  line  OC,  tlicn  the  joint 
would  be  normal  to  the  curve;  but  we  have  thought  best  in  this 
case,  to  make  the  joint  at  right  angles  to  the  director  JG.  instead 
of  the  tangent  BC;  for  this  reason  the  joint  will  be  plumb,  or 
perpendicular  to  a  horizontal  surface  when  the  wreath-piece 
is  elevated  into  position:  then  if  the  wreath-piece  be  required  to 
miter  into  a  cap,  the  easing  in  the  wreath-piece  can  be  forced  at 
right  angles  to  the  joint. 

The  bevel  applied  at  section  B,  is  found  in  the  angle  at  7, 
Fig.  7.  Observe  the  bevels  in  this  case  do  not  cross  the  tangents. 
If  the  rail  be  required  to  miter  into  a  cap,  as  shown  at  Fig.  9, 
then  return  to  Fig.  7,  make  EU  equal  the  amount  required  for 
miter  [1%^^J,  as  shown  at  Fig.  9;  through  U,  and  parallel  io  AR, 
draw  Z7/S;  prolong  KE  to  V;  return  to  Fig.  8,  and  prolong  KC 
on  face-mould.  Fig.  8,  to  equal  EV,  Fig.  7,  as  C  13;  draw  the 
joint  parallel  to  5  G,  draw  5  11  and  6  12  parallel  to  C  13  for  the 
amount  of  wood  required  to  make  the  miter. 

Observe  at  Fig.  7.  tlie  tangent  KV,  drops  below  the  horizon- 
tal line  at  U;  this  will  cause  the  block  pattern  at  section  B,  to  be 
raised  up  the  distance  UV,  above  the  centering  of  the  plank  at 
that  joint. 

This  niethocl  of  inclining  the  lower  tangent  at  the  newel,  allows 
the  wreath-piece  to  fall  lower  so  as  to  accommodate  a  shorter  newel 
post,  but  must  not  incline  too  mucli,  as  the  wreath-piece  should  ease 
off  into  the  cap,  graceful  as  possible. 

Six  [0^^]  inches  is  allowed  on  shanks  for  straight  wood,  and 
must  be  deducted  from  the  lengths  shown  in  elevation.  Fig.  2, 
Plate  31,  when  jointing  the  straight  rail. 

Fig.  9.  Shows  tlie  plan  of  the  turnout  and  the  three 
swelled  steps. 

The  treads  on  the  circle  arc  spaced  off  equal  to  the  regular 
treads,  and  graduated  on  the  wall  string,  as  shown.  The  nosings 
may  be  curved  by  using  a  pliable  strip  thinned  down'  at  one  end; 
the  nosings  at  the  wall  strings  should  be  at  right  angles  to  the 
strings. 

This  drawing  should  1)e  jijade  full  size  on  suitable  paper,  then  the 
outline  of  steps  can  be  transferi-ed  to  the  platik  by  priclcing  through 
tlic  paper  with  an  awl;  also,  the  stair-builder  can  draw  the  face- 
mould  on  the  same. 


PLATE  33. 


Plate  33.  [Scale  5^'^=1  foot].  ExhihUs  the  treatment  of 
the  cylindrr^  Fi;i.  .?,  Plate  .7/,  irlica  the  outer  or  front  strimj  is  of 
hard,  unixl,  and  the  ciiUndcr  is  i^eneered. 

Fig.  1.  Shows  the  length  of  staves  for  the  cylinder.  Fig,  4, 
Plate  31;  laid  oiT  in  tlie  same  way  as  has  been  explained  for  a  7''-' 
and  12''  cylinder. 

^Fig.  2.  Shows  tiu' cylinder  24^' diameter,  the  veneer  is  to  be 
bent  over  a  drum,  and  tiii;  staves  1,  2,  3,  glued  on  the  back  with 
the  joints  )icr))eiiuicular  to  tlie  treads.  At  A  and  B,  is  shown 
the  splice  couiiecting  the  straight  part,  and  is  intended  to  be  glued 
and  screwed  from  the  back,  as  shown. 


Plate  33.  155 

Pig.  3.  Shows  the  veneer.  AS  is  the  stretchout  of  semi- 
circle, draw  AD  and  BE  perpendicular  to  AB;  from  the  center 
C  set  off  Xo.  16  rise  Hy^,  and  Xo.  17  rise  5>4^^^;  then  elevate 
Nos,  15,  14,  18  and  19  risers  and  treads,  making  Xo.  It)  rise  6  }<'''' 
from  the  spring  line  AD,  and  Xo.  14  rise  5%^^  from  the  spring 
line  LE. 

The  joints  to  connect  the  straight  strings  are  made  at  Xo.  14 
and  19  rise;  the  veneer  is  made  the  same  thickness  throughout, 
and  the  staves  1,  2,  3,  &c.,  are  shown  extended  beyond  the 
veneer  to  allow  for  trimming  off,  and  to  have  room  for  a  screw  to 
bring  the  stave  and  veneer  down  close  on  the  drum.  At  Gf  and 
F,  the  stave  is  shown  wiiler,  and  should  be  glued  to  the  veneer 
before  bending  over  the  drnm;  keep  the  joint  of  stave  to  the 
springing  lines  AD  and  LE;  after  the  two  staves  G  and  F,  have 
been  glued  to  the  veneer,  and  the  glueing  is  thoroughly  dry, 
dampen  the  veneer  with  hot  water;  then  clamp  one  end  to  the 
drum,  being  careful  to  keep  the  spring  line  on  the  veneer  over 
the  spring  line  on  the  drum.  Then  bend  the  veneer  over  the 
drum  gently,  and  at  the  same  time  screwing  down  a  stave  at 
intervals  temporarily,  to  bring  the  veneer  down  close  to  the  drum; 
if  the  other  spring  line  agrees  with  the  spring  on  the  drum,  then 
clamp  fumly  to  the  drum,  and  leave  stand  until  the  veneer  is  dry, 
then  glue  and  rub  the  staves  to  place,  using  a  screw  at  each  end 
to  bring  all  down  firm. 

This  makes  clean,  nice  work;  the  tread  and  rise  is  cut  out, 
after  being  lifted  from  the  drum.  When  laving  off  the  lines  on  the 
veneer  use  a  lead  pencil;  if  a  knife  be  used  there  will  be  danger  of 
causing  the  veneer  to  kink. 

Fig.  4.  Shnu-t;  another  method  of  doing  the  same  thing  by 
benOinij  the  i^cnecr  AA  over  a  drum  B;  then  kertinrj  and  steam- 
ing the  hacJi  jmrt  CC,  and  hending  it  over  the  veneer. 

In  this  case  the  back  part  CC  must  be  of  an  even  thickness 
throughout,  say  IK^',  and  the  kerfs  should  be  extended  beyond 
the  springing  lines  as  shown,  and  to  within  Jg'^  of  the  back,  if 
possible;  the  kerfs  must  be  cut  perpendicular  to  the  treads,  and 
made  from  straight-grained  stuff";  the  kerfed  part  should  be  well 
softened  by  steaming,  then  bent  over  the  drum  and  let  stand  until 
dry,  being  careful  to  have  the  springing  lines  on  the  kerfed  part 
parallel  with  the  spring  lines  on  the  drum.  After  it  has  set,  lift 
from  the  drum,  tack  on  two  braces,  then  soften  the  veneer  and 
bend  over  the  drum,  being  careful  to  keep  the  plumb  lines  on  the 
veneer  to  the  spring  lines  on  the  drum;  leave  the  veneer  in  this 
way  until  dry;  then  glue  and  clamp  the  kerfed  part  down  firmly 
to  the  veneer.  Tfie  distance  apaH  to  m^ake  the  kerfs  so  as  to  close 
is  shown  next. 

Fig.  5.     fScale  H^^  equals  1^] 

Take  a  strip,  the  thickness  being  equal  to  the  thickness  of 
plank  intended  to  be  kerfed,  say  IJ^'';  run  a  gauge  line  on  to 
whatevH'r  is  allowed  to  remain  solid,  say  }4^^,  shown  by  the  dotted 
line  AB;  then  make  a  kerf  OC  with  the  saw  that  is  to  be  used 
for  the  kerfing.  Xow  draw  the  arc  of  a  circle  DE  to  whatever 
radius  required,  in  this  case  12  \"^;  then  through  the  center  O 
draw  a  straight  line  DO,  and  place  the  strip  to  the  line,  keeping 
the  kerf  to  the  center  at  O:  now  fasten  with  two  nails  at  2  and  3; 
then  move  the  other  end  i'' until  tlie  kerf  will  close,  and  mark  the 
edge  of  strip  cutting  the  arc  at  H,  then  DH  will  be  the  distance 
apart  to  space  off  the  kerf.  The  saw  should  liave  guides  clamped 
to  the  sides,  so  the  kerfs  will  be  all  the  same  depth,  for  good 
work. 


15C  Pl-ATK   33. 

Pig.  6.  Shows  another  incthod  for  constrnoA'infj  the  cyl- 
inder. 

Tlie  piece  intended  to  bend  over  the  drum  BB  to  form  the  cylin- 
der should  he  straight  in  the  grain,  and  be  made  of  an  even  thiclcness 
throughout.  The  dadoes  are  cut  perpendicular  to  the  treads,  and  all 
to  the  same  depth.  This  is  very  speedily  and  neatly  done  on  the  saw 
table  witli  a  dado  head.  The  piece  to  be  dadoed  can  be  arrauged 
across  the  table  to  the  proper  inclination  in  a  frame,  and  in  a  few 
minutes  the  woik  is  done.  One  or  two  grooves  .should  l)e  cut  lieyond 
the  spring  lines  CC,  as  shown.  Tliis  is  done  to  prevent  too  sudden  de- 
part ure  from  the  straight  to  the  circular  part,  and  thus  avoid  per- 
haps fracture.  The  string  should  be  laid  out  with  a  pencil  .so  as  not 
to  aliraid  tlie  surface,  us  that  may  cause  fracture  or  kinks.  Tlie  lay- 
ing out  sliould  be  done  before  bending,  but  not  cut  out  until  the  work 
is  lifted  from  the  drum. 

After  the  dadoing  is  done  the  work  require  to  be  well  softened  by 
by  steam  or  hot  water;  a  steam  box  is  very  handy  and  economical  for 
work  of  this  kind.  By  turning  on  tlie  live  .steam  the  work  is  soon 
softened,  and  the  moisture  is  speedily  evaporated  from  the  worlc. 
After  tho  worlc  is  sufficiently  softened  clamp  one  end  to  the  drum, 
keeping  the  spring  lines  opposile,  and  gently  bend  over  tlie  drum, 
adding  a  stay  every  few  inches  to  avoid  kinks,  and  clamp  tho  other 
end  firmly  to  tlie  drum,  being  sure  the  spring  line  on  the  work  comes 
opposite  or  parallel  to  the  spring  line  on  the  drum. 

Now  .size  the  dadoes  willitliin  glue,  and  leave  the  work  in  tliis 
shape  to  dry  out.  Then  fit  hard  wood  Iveys  into  the  grooves,  glue  and 
drive  them  in  lightly,  not  too  liard,  as  the  woric  may  raise  off  the 
drum  and  cause  kinks.  After  the  glue  is  hard  dress  off  the  keys  to 
the  curve;  then  glue  and  nail  on  tlio  back  of  cylinder  two  lines  of 
haxd  wood  strips  J4,"  thick  and  2"  wide;  one  line  %"  from  the  lower 
edge,  and  tlie  otlier  near  the  internal  angle  of  the  tread  and  rise. 
The  strips  laminated  in  two  thicknesses  would  be  be.st,  as  shown  at  2 
and  3. 

Tho  distance  apart  to  make  the  dadoes  and  the  thickness  of 
veneer,  or  solid  part,  is  explained  for  Plate  28,  Fig.  6. 

This  treatment  of  circular  strings  for  any  circle  over  10"  radius 
makes  good  and  substantial  worlv.  AH  circular  wall  strings  should 
be  constructed  in  this  way.  c 

Fig.  8.  Shows  tlie  lower  end  of  cylinder  increa.'^od  in 
thickness  to  form  grounds  for  plastering  and  offer  solid  nailing 
for  a  heavy  plaster  moulding  D;  S  shows  the  lagging  glued  on 
to  the  back  of  cylinder,  and  the  monlding  D,  is  shown  one-half 
full  size;  J' shows  the  veneer;  A,  the  stave,  and  C,  the  plaster- 
ing. This  heavy  moulding  will  have  to  be  constructed  same 
as  the  wreath-piece  of  a  hand  rail,  and  tit  to  the  cylinder  in  the 
shop  and  ptit  up  after  the  plastering  is  done. 

At  Fig.  7,  the  tangents  AB  and  BC  are  shown  for  tho 
plaster  moulding  D,  the  radius  for  the  center  of  which  Is  IK'''' 
more  than  the  radius  of  cylinder,  or  13}4^\ 

Fig.  9.    Shoivs  the  eUvation  of  ttmnents;  they  are  folded. 

Let  XX  indicate  the  edge  of  drawing  board.  Make  AB 
equal  OA,  Fig.  7,  [1.3^'^];  perpendicular  to  XX,  draw  AC  and 
BD  indefinite;  anywhere  on  XX,  place  the  ]>itcliboard,  and  draw 
the  inclination  indefinite,  cutting  AC  at  JS,  and  BB  at  F; 
return  to  Fig.  3,  draw  CJ  perpendicular  to  the  treads,  and  to 
intersect  the  inclination  GF  at  J;  from  J,  and  perpendicular  to 
EL  prolonged,  draw  JK;  then  KL  is  the  height  tliat  the  wreath- 
piece  will  raise  for  tlie  quarter  circle  from  A  to  C,  Fig.  7.  Now 
make  EC  ecpial  the  height  KL,  Fig.  3;  perpendicular  to  AC, 
draw  CD  prolonged,  intersecting  EF  prolonged  at  G;  from  D, 
and  perpendicular  to  GE,  draw  DH;  parallel  with  CD,  di-aw 
FJ;  draw  DJ  indefinite;  From  E,  and  at  right  angles  to  DJ, 
draw  EK\  make  B  3  equal  half  width  of  the  plaster  moulding 
[33^^^];  parallel  with  BD,  draw  the  half  width  of  moulding, 
cutting  the  tangents  FE  and  DJ,  at  3  and  4;  Parallel  with  XX, 
draw  EL  indefinite;  make  EL  equal  the  chord  AC,  Fig.  7;  make 
JM  equal  JC. 


J'l.ATK  3:>.  157 

Bevels.  From  the  odi^^e  of  board  XX,  rnn  the  gango  line 
ab;  perpendicular  to  XX,  draw  Z)/ equal  to  tlie  radius  OA,  Fi^'. 
"i",  iX'^y/'),  Make  Z) A  equal  DH,  and  bg  equal  ^iT;  draw  fh 
and  /g-  prolonged,  to  XX  for  convenience  when  setting  the 
bevels. 

Fig.  10.    Shoiostlic  face-mould. 

At  any  convenient  place  on  the  pattern  paper,  lay  down  the 
steel  square,  and  draw  the  right  angle  JHC  indelinito.  Make 
HF  and  HE,  each  equal  HF  and  HE,  Fig.  9;  with  F  for  a 
center,  and  DJ,  Fig.  9,  as  a  radius,  draw  arc  intersecting  HC  at 
C;  Connect  FC;  parallel  with  FC  and  FE,  draw  EO  and  CO, 
establishing  the  center  0,  and  the  parallelogram  OEFC,  on  the 
cutting  plane. 

Proof.  The  diagonal  OF  must  equal  the  distance  LM,  Fig. 
9,  if  so,  the  angle  of  tangents  at  F  is  correct. 

Make  EN  equal  FG,  Fig.  9;  draw  NO  prolonged;  through 
O,  and  at  right  angles  to  ON,  draw  PQ  for  the  position  of  tram- 
mel; make  joints  at  J" and  C,  at  right  angles  to  the  tangents  JF 
and  FC.  Make  O  2  equal  the  radius  OA,  Fig.  7  [V.',}4J']-  Let 
2  .^  and  2  4,  each  equal  the  half  width  of  moulding  (2,V^);  make 
C  5  and  C  G,  each  equal  F  3,  Fig.  9,  and  E  ~  and  E  8,  each 
equal  D  4,  Fig.  9;  parallel  with  JF,  diaw  8  10  and  7  9  -^or  the 
shank. 

Now  pivot  the  trammel  at  O,  and  trace  the  elliptic  curves  of 
face-mould  as  has  been  described  for  the  preceding  Plates.  At 
R  and  iS,  the  bevels  are  shown  applied  to  cross  the  tangents;  the 
block  pattern  shows  the  twist  of  rail  and  the  thickness  of  plank 
required;  the  shaded  parts  show  the  surplus  wood  to  be  removed. 

Pigs.  11  and  12.  Show  another  method  hoiv  to  conMruct 
the  wraith  part  of  viouldlng  hy  making  both  tajigcnts  eqxiol,  and 
using  a  cripple  joint  at  the  shank. 

Fig.  11.    Shoivs  the  elevation  of  tanoc?its ;  they  are  folded. 

Let  XX  indicate  a  base  line;  make  AB  equal  DC,  Fig.  7; 
draw  AC  and  BD  perpendicular  to  XX;  draw  the  inclination  of 
the  center  line  of  rail  as  EZi  make  EC  equal  the  height  LK^ 
Fig.  3;  draw  CD  and  EL  parallel  to  XX;  EL  cuts  BD  at  N; 
bisect  ND  at  F;  connect  CF;  draw  FE  prolonged;  make  EL 
equal  the  chord  AC,  Fig.  7.  From  the  center  D,  draw  arc  to 
tangent  FC  as  DH;  join  HC  for  the  bevel  for  both  joints;  par- 
allel to  BD,  draw  the  half  width  of  rail  to  intersect  FE  at  3. 
On  EZ,  set  off  C/''  to  >S  for  shank:  make  joint  at  S  perpendicular 
to  EZ;  prolong  FE  to  allow  over  wood  for  cripple  joint,  say  to 
J;  through  J,  draw  4  5  perpendicular  to  FJ  tor  a  temporary 
joint  on  shank. 

Fig.  12.    Shoivs  the  face-mould. 

Make  £^C  equal  CL,  Fig.  11;  with  Cand  Etor  centers,  and 
.E'JF',  Fig,  n.  as  a  radius,  draw  arcs  intersecting  at  J* and  0;  draw 
FE,  FCEO  and  CO  for  the  parallelogram  OEFC  on  the  plane  of 
plank.  Proof,  The  diagonal  OF  must  equal  the  diagonal  OB 
on  plan  Fig,  7;  if  so,  the  angle  of  tangents  at  -Pmust  be  correct; 
prolong  FE  to  J,  equal  to  EJ,  Fig.  11.  Prolong  the  radial  lines 
OC and  OE  indefinite;  make  Joints  at  Cand  J" perpendicular  to 
the  tangents  FC  and  FJ;  make  C  5  and  C  6,  also  E  7  and  E  S 
each  equal  F  3,  Fig.  11.  As  both  tangents  in  elevation  are  tlie 
same  length  in  this  case,  the  diagonal  Oi^  becomes  the  direction  of 
minor  axis.  Make  O  2  equal  OA,  Fig.  7,  for  the  semi-minor  axis, 
Let  2  3  and  2  4  each  equal  the  half  width  of  rail  (2^^).     Now 


Ifts  ' Plate  34. 

pivot  the  trammel  at  0,  with  tlie  arms  at  riglit  angles  to  0  2;  then 
set  from  pencil  to  minor  pin  on  tlie  rod  to  equal  O  4,  and  place 
llie  pencil  in  the  point  at  6,  then  slide  the  major  pin  until  both 
pins  drop  into  the  grooves,  then  fasten  the  major  pin  and  trace 
the  curve  for  tlie  convex  side  of  mould  through  the  points  6,  4,  3; 
proceed  in  like  manner  to  trace  tlie  curves  for  tlie  concave  and 
center  lines  of  face-mould  ;  draw  7  9  and  8  10  parallel  to  EJ. 

Sections  R  and  /S  sliow  the  bevels  applied.  Observe  the 
block  pattern  is  first  applied  the  same  distance  down  from  the 
face  of  crook  at  botli  joints;  then  work  off  the  sides  of  shank  to 
the  joint  bevel;  afterwards  apply  the  cripple  bevel  shown  in  the 
angle  at  4,  and  cut  the  cripple  joint.  See  first  that  all  lines  on 
tlie  temporary  joint  are  squared  over  from  the  joint  on  to  the 
upper  and  lower  and  also  the  vertical  sides  of  shank,  so  that 
when  the  temporary  joint  is  cut  away  the  lines  required  on  tlie 
cripple  joint  may  be  easily  carried  over  the  joint  again. 

Now  slide  the  block  pattern  down  on  the  cripple  joint  the 
distance  JS,  Fig.  11;  then  lay  off  the  direction  of  straight  mould- 
ing at  right  angles  to  the  cripple  joint,  and  ease  the  angle  to  please 
the  eye,  and  fit  the  lower  end  of  string. 


PLATE  34. 

Plate  34.  ErhiMts  a  tivo-story  stnir-cnse  with  n  half  pace 
winding*  in  the  fimt  flight,  (tnd  <t  doul>lc  qjutrtcr  pace  ^vindi■)UJ 
Jlifjht  in  the  second  stm-y.  Figs.  1  to  4,  are  drawn  to  a  }i^^  scale 
[scale  H^^^^l  foot];  and  Figs.  5  and  C>  arc  dnnvn  to  a  %''  scale 
[scale  %^^=1  foot]. 

The  height  of  first  story  from  top  to  top  of  joist  is  11'  4''^; 
the  hall  is  C/  0^'  wide  in  the  rough;  the  joist  is  9'^  deep  in  tlie 
second  story;  tlie  back  door  under  stairs  is  6'  6^'  high;  and  there 
is  IC  8^'  at  tlie  starting,  and  at  the  landing  5^  2>"  to  tlie  door 
jamb. 

The  height  of  second  story  from  top  to  top  of  joist  is  10'  0''; 
depth  of  joist  in  the  third  tlf)or  equals  9'';  the  soffit  of  stairs  will 
clear  the  window  in  the  second  story  as  they  land  with  a  (piarter 
pace  winding,  and  tlie  window  is  set  plumb  over  tlie  opening 
lielow  on  the  one  side;  the  horizontal  space  between  the  walls  for 
the  stairs  equals  If  4''. 

The  newel  is  l^'^/l",  to  be  set  in  the  center  of  hall;  size  of 
rail  4''X2K^^;  balusters  2''X3";  height  of  base  exclusive  of  tlie 
moulding  is  8''  for  the  first  story,  and  7''  in  the  second  story. 

fig.  1.    Shows  the  plan  of  the  first  flight. 

The  lieight  of  stoi-y  is  11'  0",  which  rednced  to  inches  equals 
136",  divided  by  17  risers  [136'''---17=8"]  equals  8"  for  each 
vise,  if  we  allow  25"  for  a  constant,  the  relative  proportion  of 

*Thc  plan  of  the  a'oove  stair-case  is  not  intended  as  a  model  for 
the  young  man  to  copy  from  in  practice,  for  wiudeis  iu  small  and 
contracted  halls  are  objectionable,  and  sliould  be  avoided  at  all 
times  if  possible.  The  grand  circular  or  elliptical  stair-case  can  he 
made  an  object  of  beauty,  that  cannot  be  excelled  in  stair-casing, 
In  that  ciise  having  more  room,  the  winders  can  be  increased  in 
width  at  the  outer  string,  and  thus  give  to  the  rnil  easy  flowing 
curves,  and  a  gentle  ascent  to  the  grade  of  steps;  but  as  the 
stair-builder  has  to  adapt  the  stair-case  to  the  space  allotted,  hence 
he  will  have  to  exercise  his  judgment  as  to  what  will  suit  the  space, 
and  give  the  best  I'esulls;  the  above  plan  Is  given  as  an  extreme,  and 
is  intended  1o  sliow  liow  such  stairs  may  be  treated,  the  principle 
being  the  same  for  all. 


Plate  3-i.  159 

tread  to  rise  will  equal  9^^  pr/^— (8'^+8''=16^')=9^^],  then  the 
pitch  ot:  stairs  for  the  lirst  flight  will  equal  8'^X9'^,  if  there  be 
roum  to  allow  a  tread  equal  to  9i". 

The  well  hole  is  in  the  center  of  hall,  and  the  cylinder  is  S'' 
diameter,  the  winders  should  be  laid  off  on  heavy  paper.  First 
lay  oit'  the  line  of  rough  walls-,  parallel  with  the  walls,  draw  the 
wall  strings,  allowing  ";i"  for  plaster  on  brick  walls,  and  14,"  on 
stud  partitions,  then  %"  for  the  thickness  of  base,  making  \%" 
lor  the  stud  partition  wall,  and  \%"  for  the  brick  walls,  that 
niust  ))e  allowed  from  the  rough  walls  to  face  of  the  wall  strings; 
the  thickness  of  wall  strings  is  usually  \%",  this  thickness 
allows  sufficient  to  work  the  grounds  on  the  solid  for  the  plaster- 
ing. 

Draw  the  cylinder  in  the  center  3''  Q"  from  the  walls;  draw 
the  outer  string;  set  ott'  in  tins  case  from  the  string  line  \\"  for 
the  regular  tread  line  around  the  cylinder.  Right  here  the  work- 
man may  have  to  make  several  trials  in  spacing  off  the  winders 
on  the  walking  line,  either  shifting  the  walking  line  further  out, 
or  bringing  it  nearer  to  the  well  hole,  so  as  to  locate  the  first  rise 
to  admit  an  easing  and  the  finish  around  door  at  the  starting; 
the  walking  line  should  not  be  over  18'^  from  the  string  line,  and 
may  be  located  at  any  point  between,  the  nearer  to  the  string  line 
the  better,  as  then  the  winders  at  the  narrow  ends  will  be 
increased  in  width. 

Now  with  the  dividers  set  to  %"  begin  at  the  center  (No.  13 
rise)  of  semi-circle,  and  space  off  towards  the  starting  11  threads 
on  tlie  walking  line,  which  leaves  about  18''''  from  No.  1  rise  to 
the  face  of  door-jamb,  to  allow  for  the  "trim"  and  easement  on 
the  wall  string.  Also,  step  off  towards  the  landing  five  (5)  full 
treads,  and  we  have  9'^  from  the  face  of  No.  17  rise  to  tlie  door- 
jamb;  this  is  too  scant  if  it  could  be  avoided,  but  less  has  to  do  iu 
many  cases. 

In  all  cases  for  a  half-pace  Vi^iuding  stairs  at  the  center  (No. 
13  rise)  there  should  be  a  rise,  or  the  center  of  a  tread.  In 
locating  the  risers  at  the  outer  string  first  space  off  the  balusters 
around  the  cylinder,  beginning  at  the  center  of  cylinder  (Xo.  12 
rise  in  this  case),  and  spacing  them  equal  to  half  a  tread  or  less; 
in  this  case  they  are  less,  so  the  balusters  will  appear  evenly 
spaced.  Nos.  8,  9,  14  and  \h  threads  may  be  graduated  to  help 
the  easing  on  the  lower  edge  of  string,  while  the  balusters,  iii- 
slead  of  being  over  the  rise,  may  sit  over  on  the  treads  to  show 
them  evenly  spaced,  as  shown  at  step  No.  17,  Fig.  16,  Plate  15. 
In  stairs  cramped  for  room  this  has  to  be  done.  When  the  points 
for  the  risers  are  spaced  off  on  the  cylinder  and  front  string  to 
connect  the  "llyers"  or  straight  treads,  then  draw  the  face  of 
risers  to  suit  the  balusters  and  through  the  points  just  found  on  the 
walking  line  to  intersect  the  wall  string.  It  will  be  observed  the 
rise  Nos.  11  and  13  do  not  radiate  to  the  center  of  cylinder,  and 
Nos.  9,  10,  14  and  15  cut  the  front  string  very  obli(iue.  This 
should  be  avoided  whenever  possible  to  do  so  by  allowing  llie 
risers  to  radiate  from  the  center  of  cylinder  and  allowing  but  one 
graduating  sl«*p  outside  the  cylinder.  This  case  has  been  intro- 
duced to  give  the  learner  an  idea  how  to  manage  a  flight  when  the 
steps  have  to  be  crowded.  In  small  buildings,  for  want  of  space, 
the  stairs  are  often  too  much  crowded. 

Observe,  that  the  temporary  step  patterns  for  Nos.  8,  9,  10 
and  11  winders  will  answer  for  Nos.  1.5,  14,  13  and  12  winders  by 
reversing  the  patterns.  For  tlie  trimming  of  the  well  in  the  second 
story,  allow  %"  from  the  back  of  No.  17  rise  to  the  joist,  or  ^/  ^" 
from  the  wall,  as  shown.     The  width  to  trim  the  well  ia  the 


160  Plate  34. 

secoud  story  at  the  starting  of  the  second  flight  will  equal  the  half 
width  of  hall  (S'  0'''')  plus  the  radius  of  cylinder  (4^^),  and  the 
thictness  of  fascia  (1^0  [^^  0^^-t-4^^4-l^J=3''  5^^J  equals  3'  5^'  as 
shown  on  plan. 

The  trimmer  at  the  starting  of  secoud  flight  should  be  at  the 
back  of  cylinder,  and  at  right  angles  to  the  wall,  if  that  will  allow 
enough  head  room.  In  this  case  there  will  be  ample  head  room, 
the  face  of  trimmer  being  over  the  middle  of  first  tread,  thus 
allowing  the  ceiling  to  carry  around  level  to  back  of  cylinder 
starting  in  the  second  flight,  and  at  right  angles  to  the  level  fascia. 
The  soffit  of  the  second  flight  will  then  curve  down  at  right  angles 
to  the  face  string,  instead  of  following  the  twisting  line  of  treads 
and  risers.  The  face  of  trimmer  is  sliown  F/  1}-^''^  from  the  face 
of  joist  at  the  lauding,  or  8'  i^i'^  from  the  wall;  the  lauding  v/ill 
theu  be  trimmed  out  to  2''  T^''  by  3^  Tri" ^'  in  the  rough. 

The  dotted  lines  show  the  manner  of  jiutting  in  the  Ijearers; 
dry  3'^  by  4^'  scantling  should  be  selected  for  this  purpose,  neatly 
cut,  fit  aud  well  nailed,  aud  rough  brackets,  with  the  grain  per- 
pendicular to  the  treads.  The  brackets  are  nailed  to  the  bearers, 
aud  through  the  back  of  rise  into  the  tread. 

Fig.  2.     Shoics  the  elevation  of  threads  and  risers. 

AB  shows  the  story  rod;  the  height  of  story  11'  4^^  is  divided 
into  17  risers;  the  first  length  (6'  8'^)  to  measure  for  the  straight 
rail  is  shown  taken  from  the  spring  of  turnout  to  the  spring  of  cyl- 
inder. No.  2  length  (2''  V^  is  taken  from  the  spring  of  cylinder 
to  plumb  with  the  face  of  last  rise.  No.  17,  aud  the  length  of  level 
(3''  9'^)  is  taken  from  the  face  of  No.  17  rise  to  the  spring  of  cyl^ 
iuder  starting  of  the  second  flight. 

Fig.  3.    SJioxvs  plan  of  the  flight  landiwj  in  the  tliird  story. 

The  height  equals  10'  C,  being  reduced  to  inches  equals 
120''',  aud  divided  by  15,  the  number  of  risers  for  a  trial,  equals 
i"  for  each  rise,  and  the  relative  width  of  thread  will  equal  9". 

The  well  will  be  trimmed  to  the  width  of  that  in  the  second 
story  3'  5"  wide,  and  the  space  between  the  walls  is  11'  4"; 
allowing  the  space  for  the  second  flight  to  equal  11'  4"  by  3'  5"  in 
the  rough.  Allow  3'  0"  at  each  of  the  quarter  pace  winders  to 
the  center  of  cylinder,  phis  43'o"  for  j^raduating  the  treads  at  the 
spring  of  cylinders  (3' 0"+3'  0"+4ii"-f4>^"=6'  9"),  which 
equals  6'  9"  to  be  deducted  from  the  whole  space,  11'  4"  (11'  4" 
—6'  9"z=4'  7")  equals  4' 7",  to  be  divided  by  the  width  of  a  tread, 
(9")  gives  us  six  straight  treads;  that  will  place  a  rise  in  the  cen- 
ter of  well.     In  this  case.  No.  8  rise  comes  in  the  center. 

We  will  make  the  walking  line  14"  from  the  face  of  front 
string  ou  trial. 

Now,  with  the  dividers  set  to  the  width  of  a  tread  (9"), 
begin  at  No.  8  rise  and  step  off  the  treads  either  way  ou  the 
walking  line;  the  face  of  Nos.  1  and  15  rise  comes  on  line  witli 
the  face  of  level  front  string.  This  will  answer  very  well;  from 
No.  .5  and  No.  11  riser,  space  off  tlie  balusters  in  the  cylinder  to 
equal  the  spacing  of  tlie  balusters  on  the  straight  steps  (4K'''') 
or  a  little  less  in  small  cylinders.  Tlie  spaces  in  this  case  are  less. 
Nos.  1  and  15  rise  should  be  curved  to  suit  the  circular  nosing 
without  too  much  peak  at  the  point  of  miter,  and  also  help  the 
easing  at  the  joining  of  the  cylinder  with  the  level  string.  It 
will  bo  observed  that  Nos.  4  aud  11  winders  are  the  same,  only 
reversed.  The  front  of  the  former  is  back  of  the  latter,  and  one 
set  of  patterns  will  srnswer  for  the  winders  of  both  quarter  paces 
in  tliis  case,  thus  saving  time  aud  material  when  cutting  tliem 
from  the  plank,  aud  also  adds  to  the  general  appearance  of  the 
stairs. 


Platj:  ?a.  161 

After  the  measures  arc  taken  for  stairs  of  this  kind,  the  first 
thing  the  stair-builder  sliould  do  is  to  make  a  plan  to  a  scale  of 
say  K*"  to  equal  one  foot.  By  so  doing  fewer  mistakes  will  occur, 
and  much  time  be  saved. 

For  the  head-room.  Count  down  from  tlie  landing  12 
risers  at  8^^  each  equals  96^^  (H|/^=8'  0^^)  equals  8'  0'^,  minus 
the  joist,  flooring  and  plastering,  say  11^^  will  equal  7^  \"  from 
the  top  of  No.  3  step  to  the  line  of  ceiling;  this  will  answer. 

Fig.  4.    Shoivs  the  dcvatioyis  of  treads,  risers  and  strings. 

The  story  rod  AB  is  divided  into  15  risers.  SSS,  &c.,  show 
the  springing  of  the  cylinders.  The  measure  for  cutting  the 
straight  rail  is  shown  taken  from  spring  to  spring  of  cylinder. 
No.  4  length  is  shown  7'  0M^^  and  No.  5  length  (6'  7^^)  is  taken 
from  the  spring  of  cylinder  landing  to  spring  of  quarter  cylinder, 
and  from  quarter  cylinder  to  wall  3^  0''^  measured  on  plan.  The 
raking  lengths  are  taken  at  tlie  bench,  and  the  level  lengths  after 
the  stairs  are  stepped  up,  and  all  entered  in  the  order  book. 

Fig.  5.  Exhibits  plan  of  No.  1  cylinder,  [Scale  %'^=V\ 
Showing  the  angle  that  the  steps  and  risers  make  with  the  outer 
string  and  cylinder.  The  nosing  line  is  drawn  parallel  with  the 
risers,  and  intersects  with  the  nosing  line,  which  is  drawn  par- 
allel with  the  face  string;  the  face  of  risers  is  drawn  to  intersect 
the  bracket  line,  determining  two  points  through  which  to  draw' 
the  miters  of  nosings.  It  will  be  observed  at  No.  10  step  the 
point  of  miter  is  very  acute.  To  avoid  so  long  and  pointed  miter 
it  will  be  better  to  round  it  off,  and  connect  the  nosing  and  scotia 
of  step  with  the  return  nosing,  making  a  joint  at  right  angles  to 
the  face  string,  as  shown  at  A.  The  nosings  of  Nos.  11  and  12 
steps  are  rounded  off  to  connect  the  return  nosings. 

Fig.  6.  [Scale  ^'"=1  foot],  Shows  the  cylinder  connecting 
the  straight  string;  the  shaded  part  shows  the  staves,  the  angle 
that  the  risers  make  with  the  face  string,  and  the  cylinder,  for 
the  cut-out  of  front  string,  is  shown. 

The  joint  of  cylinder  is  y/^  from  the  cut-out  of  No.  10  rise; 
Nos.  9,  8  and  7  treads  are  4^^,  4K^^  and  9'^  respectively:  Nos.  11, 
12  and  13  rise  come  in  the  cylinder,  and  the  staves  can  be 
divided  off,  glued  up  and  trimmed  to  suit  the  direction  of  risers; 
the  joint  of  cylinder  is  1)2  ^^  from  the  cut-out  of  No.  14  rise,  and 
Nos.  14,  15  and  16  treads  are  4^^,  ^y  and  9^^  respectively. 

Fig.  7.  [%'''  Scale].  Shows  the  well  hole,  startmg  second 
flight;  tlirough  the  intersection  of  the  steps  and  risers,  with  the 
return  nosings  aud  brackets,  draw  the  miter  lines  for  the  ends  of 
steps;  No.  1  and  2  step  have  the  nosings  rounded  to  avoid  too 
long  a  miter,  and  allow  the  baluster  to  enter  the  mortise  easily. 
The  joint  of  cylinder  is  %'^  from  the  face  of  No.  4  rise. 

Fig.  8.  \}i'^  Scale].  Shows  the  width  of  staves,  they  are 
made  to  suit  the  spacing  of  the  risers;  the  spring  line  of  cylinder 
is  l}4'^  from  the  cut-out  of  No.  4  rise;  and  the  cut-out  of  outer 
string  for  No.  4  and  5  treads  are  Z}4^^  and  9^''  respectivelj',    * 

Fig.  9.  [^4^^  Scale].  Shows  the  angle  of  steps  and  risers 
intersecting  the  bracket  line  and  return  nosing;  from  those  two 
points  draw  the  miters  for  the  ends  of  Avinding  steps,  for  the  return 
nosings  and  brackets.  The  landing  and  starting  rise,  Fig.  7,  is 
made  concave  and  convex  to  help  the  width  of  cylinder  connect- 
ing the  level  fascia  or  string,  and  also  the  spacing  of  the  balusters; 
the  face  of  No.  12  rise  is  shown  !}£"  from  the  joiut  of  cylinder. 


163  Pi.AtR  S5. 

Pig.  10.  [%^^  Scale].  Shows  the  staves  lined  off  to  suit 
the  spacing  of  risers,  tlie  cut-out  of  face  string  is  shown  for  Nos. 
10  and  11  tread  to  be  0'^  and  o>.<^^,  and  the  joint  of  cylinder  is 
shown  %^^  from  the  cut-out  of  No.  13  riser.  Th.e  plan  of  winders 
should  be  drawn  fall  size  on  nianilla  paper,  and  rolled  up  until 
needed;  the  intersection  of  risers  with  the  wall  strings,  give  the 
width  of  winders,  as  shown  on  plan,  Fig.  1*  No.  8  tread  is  15^' 
from  face  to  face  of  rise,  and  No.  9  is  Sf^;  No.  10  is  8}i^^  from 
face  of  rise  to  wall  string  in  the  augle;  and  from  the  angle  to 
face  of  No.  11  rise  is  173<^^;  No.  11  and  12  treads  are  16K^^ 
each,  and  No.  l:>  tread  is  173^''^  from  face  of  rise  to  face  of  wall 
string  in  tlie  angle;  then  S}4^^  from  the  face  of  string  in  the 
angle  to  face  of  No.  14  rise;  No.  14  tread  is  31^^  and  No.  15 
tread  is  15''^  from  face  to  face  of  rise;  No.  16  tread  is  the  regular 
width  9^\ 

When  laying  out  the  wall  string,  a  very  good  way  is  to  note 
downi  these  widths  on  a  piece  of  paper,  and  thus  avoid  referring 
to  the  drawing.  The  face  strings  are  shown  to  be  1''''  thick,  and 
are  halved  on  to  the  cylinders  at  their  joinings,  and  should  bo 
glued  and  screwed  from  the  back  for  good  work. 


PLATE  35. 

Plate  35.  [Scale  %''^=l  foot.]  Shoivs  the  front  and  ivall 
stri7igs,  and  the  development  of  staves  in  the  cylinder  for  the  first 
jHilhL  of  winders,  Plate  34. 

Fig.  1.  Shmrs  the  front  string,  at  the  starting  and  landing, 
and  broken  at  the  middle,  connecting  which  is  shown  the  devel- 
opment of  staves,  as  taken  from  the  chords  shown  at  Fig.  G,  Plate 
34,  and  is  intended  to  show  how  the  length  of  staves  may  be  ob- 
tained. Tlie  stave  for  No.  10  tread  is  3^^  wide  on  the  chord;  Nos. 
11  and  12  is  3K^^  and  No.  13  is  shown  2^^     See  Fig  6,  Plate  34. 

The  face  string  is  spaced  off  with  the  dividers  for  the  regular 
treads,  as  has  been  explained  at  former  plates.  No.  8  tread  is 
43^^^;  No.  9  is  4^^,  and  the  spring  of  cylinder  AB  l^H^'  from  the 
cut  out  of  No.  10  rise;  No.  16  is  a  regular  tread;  No.  15  tread  is 
^}i^^,  and  No.  14,  ?>%'\  and  the  joint  or  spring  of  cylinder  is 
13'2^^  from  the  cut-out  of  No.  14  rise.  The  steps  are  IH^^  thick. 
It  will  be  noticed  at  the  landing  F  the  string  is  notched  li^^  to 
come  level  with  the  joist;  make  the  width  of  level  string  at  that 
point  1)^^  for  joist,  and  %^' for  plastering  (9^^-f  X'^=9X^0  equals 
*.)%^\  The  width  of  inclining  string  is  6^^  from  the  internal 
angle  of  stop  and  rise  to  the  lower  edge  of  plaster.  Opposite  No. 
15  and  16  rise  the  string  is  increased  in  width,  and  at  No.  8  rise 
the  width  is  diminished  some  to  allow  the  casings  a  graceful  curve. 

The  easings  connecting  the  staves  are  imperfect,  and  is  done 
to  get  the  length  of  staves  in  the  rough.  After  the  staves  are 
glued  up,  the  cylinder  formed  and  connected  to  the  strings,  then 
the  perfect  easings  are  made  agreeable  to  the  eye  and  taste.  A 
triangular  piece,  H,  is  glued  on  the  lower  end  to  relieve  the  acute 
angle  formed  by  the  inclination  of  the  string  with  the  floor  line 
with  an  easing.  The  easing  is  short  to  allow  the  base  board  along 
the  panel  work  to  join  flush  and  square  with  the  string.  JK 
shows  the  joint  or  spring  of  turnout  6''^  from  the  cut-out  of  No.  3 
rise. 

The  dotted  line  Jtf  shows  the  thickness  of  step  (IK^'')  Put 
off  the  lower  end  of  string,  making  No.  1  rise  6%^^  high,  so  that 


Plate  3S.  163' 

when  the  step  is  in  place  the  rise  will  be  equal  in  height  to  the 
rest. 

The  first  length  for  jointing  the  rail  is  is  6''  8'''';  the  second  is 
2'  V^;  and  the  third  is  3^  9^^  on  the  level. 

Fig.  2.     Shows  the  ivall  string  for  the  first  10  risers. 

EF  shows  a  joint;  to  make  this  string  in  one  piece  would 
require  the  plank  to  be  22'^  wide.  So  wide  a  plank  is  not  always 
at  hand  and  it  is  better  to  make  the  string  in  two  pieces.  Let  the 
piece  containing  the  winders,  take  in  so  many  regular  treads  as 
the  width  of  plank  will  admit.  In  this  case  we  have  two  and  a 
half  regular  treads  in  addition  to  the  winders,  so  we  will  make 
the  joint  EF  at  the  center  of  No.  5  tread. 

To  hud  the  bevel  C,  take  the  average  of  the  treads  by  the 
rise;  thus  add  together  the  width  of  each  tread  at  the  wall  string, 
and  divide  by  the  number  of  risers  to  be  included  in  the  string 
piece,  1 8K^^-l-31^^+15'''+9''+9''^+43'.i  ^^=65^^]  [65^^-f-5=15'^], 
equals  15''''  as  the  average  tread.  Now  with  the  steel  square  take 
15^''  on  the  blade,  and  the  rise  %''  on  the  tongue,  and  apply  from 
the  edge  FH,  of  plank.  The  tongue  will  give  the  bevel  or  plumb 
cut  shown  at  C  for  each  rise.  Now  space  off  the  risers  from  the 
plan,  Fig.  1,  Plate  34,  using  the  bevel  to  give  the  direction. 
Then  set  the  dividers  to  the  height  of  a  rise  [8^^],  and  mark  each 
rise,  and  draw  the  treads  at  right  angles  to  the  rise,  using  the 
steel  square. 

The  regular  treads  at  the  lower  end  of  string,  are  stepped  off 
on  the  gauge  line,  as  has  been  described.  The  joint  EF,  may 
either  be  lapped  or  grooved  and  tongued  in  the  joint,  and  a  strip 
nailed  on  the  face  of  string  to  hold  the  joint  firm.  It  may  be 
removed  when  the  string  is  in  place. 

At  the  upper  end  \%^^  is  added  on  to  receive  the  wall  string, 
Fig.  3,  and  a  groove  at  AB,  is  shown  to  admit  the  tongue  AB, 
Fig.  3. 

Pig.  3.    Shows  the  ivall  string  No.  2. 

The  two  center  treads.  No.  11  and  13,  are  alike  IGK'^XS^' 
rise  and  the  bevel  E,  may  be  set  to  that  pitch  for  the  direction  of 
each  rise.  The  width  of  treads  on  the  string  17^^^  IGH^^, 
H')H'',  17K^^  are  taken  from  the  plan.  Fig.  1,  Plate  34.  At  "the 
upper  end,  \%'^  is  added  on  to  receive  string  No.  4.  The  shaded 
part  CD,  shows  a  groove  )4''  deep  to  receive  the  tongue  DC, 
Fig.  4.  The  dotted  line  at  the  lower  end  shows  the  face  of  No, 
1  string,  and  K''^  is  added  on  to  allow  for  tongue. 

Fig,  4.    Shows  No.  3  ivall  string. 

The  bevel  for  the  direction  of  risers  may  be  found  by  taking 
the  average  of  the  treads,  the  same  as  for  No.  1  string.  The 
width  of  treads  on  plan  equals  8}^^^,  21'''',  1.5'^,  9''^,  plus  11^^ 
for  easment  at  the  landing;  equals  643^'^,  which  being  divided  by 
4  risers,  gives  163^ ''^  for  the  average.  Then  apply  the  steel  square 
to  the  edge  of  plank,  with  163^^'  on  the  blade  and  8^^  on  the 
tongue,  the  tongue  will  give  the  bevel  A  for  the  direction  of 
risers.  Now  line  otf  the  treads  at  right  angles  to  the  risers;  No. 
14  rise  is  8^^^  from  the  face  of  No.  2  string,  shown  by  the  dotted 
line;  DC  shows  the  limit  of  the  tongue. 

The  treads  and  risers  are  now  lined  otf  on  the  wall  strings; 
the  next  will  be  to  ease  off  the  angles  and  connect  them  in  the 
corners  with  curves  that  will  be  graceful  and  pleasing  to  the  eye. 
From  the  external  angle  of  tread  and  rise  set  off  4^^  as  shown  by 
the  arcs,  as  JZ,  Fig.  2.     Now  it  will  be  obvious,  that  at  the  lower 


164.  Pl^TE  36. 

end  of  No.  ?>  wall  string,  the  easing  to  connect  No.  2  string  must 
raise  np  sufficiently  liigh  to  clear  No.  14  rise  with  the  4''''  face 
above  the  treads  at  the  angle;  T''''  is  allowed  at  the  lauding  for 
height  of  base,  and  on  trial  we  will  set  up  ll'''  at  the  lower  end 
and  trace  the  curve  AXD  for  the  upper  edge  of  string,  using  a 
pliable  strip.  At  D  care  must  be  taken  to  have  the  curve  to  tan- 
gent a  line  at  right  angles  to  the  plumb  cut  DC. 

From  the  top  of  tread,  at  the  upper  end  of  No.  1  wall  string, 
set  up  on  trial  G}i^^,  and  trace  the  curve  for  the  upper  edge  of 
wall  string  to  tangent  the  straight  part  at  (r,  also  keeping  the 
strip  near  to  the  ares,  as  consistent  with  a  curve  agreeable  to  the 
eye. 

Now  at  the  lower  end  of  No.  2  string  set  up  6}4^^  to  agree 
with  the  easing  at  the  upper  end  of  No.  1  wall  string;  also  set  up 
11''^  at  the  upper  end  of  No.  2  wall  string  to  agree  with  the  lower 
end  of  No.  3  wall  string,  and  ease  oft'  the  angles  at  F  and  G.  As 
the  treads  iu  No.  2  wall  string  are  near  alike,  the  upper  edge  may 
be  straight.  It  will  be  noticed  that  opposite  Nos.  15  and  16  rise. 
No.  3  string,  the  curve  does  not  tangent  the  arcs,  passing  above 
the  former  and  under  the  latter.  This  cannot  be  avoided  always. 
The  stair-builder  must  make  his  curves  agreeable  to  the  eye  and 
free  from  abruptness  as  /le  possibly  can  make  them,  for  in  that 
consists  the  pride  of  his  profession. 

Tiie  upper  and  lower  edge  of  wall  string  may  next  be  trimmed 
off,  and  the  steps  and  risers  housed  in.  The  nosings  and  scotias 
for  the  straight  steps  are  marked  on  the  string  from  the  step  and 
rise  after  being  glued  up,  as  has  been  explained  for  Plate  22, 
When  marlcing  the  nosings  and  scotias  on  the  strings  for  housings, 
for  the  winders,  cut  a  piece  of  straight  nosing  to  the  oblique 
angle  that  the  winder  makes  with  the  string  for  a  pattern,  and 
trace  the  contour .  of  nosing  and  seotia  for  the  housing,  as  pre- 
viously Qxplaiued. 


PLATE  36. 

Plate  38.  [Scale  %''-=.l  foot].  Exhihits  the  front  and 
wall  fstrimis  for  the  flight  Fuj.  3,  Plate  34.  Also  the  development 
of  staves  in  the  cxjUnder  to  obtain  their  lengths  in  the  rough. 

Fig.  1.  Shows  the  lower  end  of  face  string  connecting  the 
cylinder. 

AB  shows  the  joint  of  cylinder  13^^^  from  the  cut-out  of 
No.  4  rise.  No.  4  tread  is  o}4''^  wide  on  the  face  string,  and  No. 
5  tread  equals  y^''.  The  dotted  line  AC,  shows  a  gauge  line  run 
on  6^^  from  the  lower  edge  as  a  guide  for  the  internal  angles  of 
the  regular  treads  and  risers.  The  width  of  each  stave  is  taken 
from  the  ciiord,  Fig.  8,  Plate  34.  DS  shows  the  joint  of  cylinder 
connecting  the  level  string,  which  is  9X^''  wide  to  cover  tlie 
rougli  joist  and  receive  the  plaster. 

it  will  be  noticed  that  No.  1  rise  is  7M''''  Wgh»  instead  of  8''', 
the  regular  height  of  rise.  This  occurs  from  the  step  being  13^'" 
thick,  and  the  tloor  1^^.  By  reducing  the  first  rise  }4^^,  the  first 
stave  will  then  come  close  up  under  the  flooring.  This  does  not 
reduce  the  whole  height  any,  for  it  will  be  seen  at  the  landing, 
Fig,  2,  a  K''''  1^5  added  on,  so  that  the  level  fascia  will  come  chuck 
up  under  the  iloor.  and  at  the  same  time  tkp  easing  will  drop  Ji^^ 
below  the  joist  to  receive  the  plastering. 


pLATr.  06.  16j5 

The  casing  on  the  string  and  at  the  lower  end  in  tlie  cylinder 
is  temporary,  and  intended  to  sliow  the  length  to  cut  the  staves  in 
tlie  rough.  After  they  are  glued  up  and  the  cylinder  spliced  to 
the  strings,  the  easements  can  be  better  studied,  and  the  defects 
remedied  to  please  the  eye. 

Fig.  2.  Shoics  the  clevelophient  of  staves  for  the  cylinder 
landiruj  in  the  Hard  story;  the  widths  are  taken  from  the  chords 
Fiij-  iO,  Plate  31. 

AB  shows  the  joint  of  cylinder  connecting  the  inclining 
string,  and  %'^  from  the  cut-out  of  No.  13  rise.  DC  shows  the 
joint  connecting  the  level  string.  A  triangular  piece  at  E,  will 
be  required  to  glue  on  the  lower  edge  of  level  string  to  help  tlio 
casing  at  the  joining  of  the  cylinder.  The  stave  at  No.  12  tread 
is  2M''^  wiil^;  No.  13  and  14  are  8^''  wide,  and  No.  15  is  3'^ 
wide.     The  dotted  lines  show  the  length  of  staves  in  the  rough. 

Fig.  3.    Shows  the  wall  stHng  No.  1  at  the  starting. 

No.  1  tread  is  15^^  wide,  and  No.  2  is  23'^  wide  on  tlie  w'all 
string,  as  taken  from  plan,  Fig.  3,  Plate  34.  The  part  dotted  Une 
CD  shows  the  face  of  No.  3  wall  string  connecting;  in  the  angle 
a  X'^  is  added  to  enter  the  wall  string  No.  2. 

Fig.  4.  Slwws  ivall  string  No.  2 

As  there  are  w  inders  at  both  ends,  it  had  better  be  made  in 
two  parts.  The  bevels  at  X  and  O,  for  the  direction  of  risers, 
may  be  found  in  the  same  manner,  as  explained  for  Fig.  3,  Plate 
35.  Nos.  3  and  13  rise  come  in  the  corners  in  this  case.  AB  and 
CD  show  grooves  into  which  the  tongue  on  No.  1  and  No.  3  wall 
strings  are  fitted;  EF  shows  the  splice  joint. 

Another  and  convenient  way  to  line  off  the  strings  for  veneers 
is  to  malce  an  elevation  of  each  string  to  a  scale  drawing,  as 
shown  at  Nos.  1,  2,  3,  wall  string,  then  draw  a  line  GH.  so  as  to 
divide  the  breadth  01  string  at  HG  and  EL  about  equal  at  it.s 
widest  part;  then  set  the  bevel  X,  or  O,  to  agree  with  the  riser.-: 
and  the  line  GH,  or  EL.  The  width  of  treads  is  taken  from 
plan,  Fig.  3,  Plate  31,  on  a  slip  of  paper  for  convenience.  The 
bc\el  at  B,  Fig,  5,  may  be  found  in  the  same  way.  Care  must  be 
taken  to  line  off  all  the  treads  at  right  angles  to  the  risers.  By 
drawing  the  elevation  of  treads  and  risers,  also  the  curves  on  the 
upper  edge  of  string,  to  a  scale,  the  young  man  will  gain  experi- 
ence in  tlie  use  of  the  drawing  instruments. 

At  tlie  lower  end  of  No.  I  wall  string  7^^  it  allowed  for  the 
iioight  of  base;  also  the  same  is  allowed  at  the  landing,  exclusive 
of  the  moulding. 

A  rule  for  the  width  of  base,  ir.c.uding  the  moulding,  rela- 
tive to  the  height  of  story,  is  one  inch  I'ci  tvery  foot  in  heiglit  of 
story  from  floor  to  ceiling.  A  suitable  easing  is  found  in  tliis  case 
at  the  lower  end  of  No.  3  string,  by  allowing  33<^^^  for  height  of 
string  above  No.  13  step  at  the  angle.  At  the  upper  end  of  No.  3 
string,  from  tlic  top  of  No.  13  tread  to  the  upper  edge  of  wall 
.string  will  equal  C8^'-f  3K^'=11K^'')  HX'^  This  also  allows  an 
easing  agreeable  to  the  eye. 

And  at  the  lower  end  of  No.  2  wall  string  a  suitable  easing 
is  formed,  leaving  the  siring  63-.^'''' above  No.  3  tread.  Then  the 
height  at  the  upper  end  of  No.  1  string,  above  No.  3  tread,  will 
e(|nal  H^^  for  rise,  plus  OK^^  to  connect  tlic  lower  end  of  No.  3 
string,  equals  14^'^  wliich  allows  a  favorable  easing  at  the  ui)per 
end  of  No.  1  string,  as  shown.  After  the  curves  on  the  wall 
strings  are  made,  mark  all  the  casings  on  a  board  intended  for  th<; 
mouldings,  and  thus  save  time  in  working  them  out  when  needed. 


166  Plate  37. 


PLATE   37. 

Plato  37.  [Scale  K^'=l  foot].  Exliiljits  how  to  find  the 
lenrjth  of  tatujents  and  radius  for  the  turnout  at  the  newel  past; 
also  the  face-mould  for  the  same.  Tlie  facc-mouMs  for  the  half 
pace  winding  in  tlie  first  Jiiijht,  and  the  tico  quarter  pace  wind- 
i7i;/s',  startinij  and  landing,  in  the  upper  flight,  for  the  stair-case, 
Plate  34. 

Figs.  1  and  2.  Show  how  to  locate  the  radius  of  turnout 
relative  to  the  height  of  newel  post  and  inclination  of  rail. 

The  newel  post  is  7'''X'i'^^-  Through  the  center  at  O,  draw 
the  face  of  Ko.  1  rise  perpendicular  to  one  side  of  newel;  extend 
the  side  of  post  by  a  line  to  A,  as  CA,  for  the  center  of  rail  shov  n 
Ijy  the  dotted  line.  Parallel  with  No.  1  rise,  draw  No.  2  and  3  ri-< . 
Now  draw  a  base  line  XX,  Fig.  3,  and  ele\ate  No.  1,  3  and  o 
rise.  Through  the  center  of  baluster  O,  O,  draw  the  under  side 
of  rail,  and  parallel  with  00,  draw  the  center  of  rail  AB 
indefinite. 

From  the  top  of  No.  1  step  set  up  6'^  to  the  under  side  of 
rail,  and  IK^' additional  to  the  center  of  rail,  (G'^+lii'^^=7K''\ 
equals  731^^  from  the  top  of  No.  i  step  to  tlie  center  of  rail  at  F: 
from  JP,  and  parallel  to  XX,  draw  a  line  1o  intersect  the  inclina- 
tion of  rail  at  S;  from  B,  let  fall  the  perpendicular,  intersecting 
the  center  line  of  rail,  Fig.  1,  at  C;  draw  CO,  intersecting  the 
cap  at  D. 

Make  CE  equal  CD  for  the  length  of  tangents  on  plan. 
Perpendicular  to  the  tangents,  and  from  the  points  E  aiul  D, 
draw  the  radial  lines,  converging  at  F:  with  FE  as  a  radlu-^, 
draw  the  curve  for  the  center  line  of  rail  from  E  to  D.  Now 
draw  the  string,  bracket  and  nosing  lines,  and  miteis  con- 
necting the  return  nosings,  thus  completing  the  plan  of  turnout 
for  getting  out  the  steps.  The  face  of  No.  3  rise  is  shown  C' 
from  the  spring  of  turnout;  the  face  of  string  is  the  solid  Hue  on 
plan. 

Fig.  3.     Shows  the  j>l<tn  of  tangents  for  i}\e  ftice-nwxdd. 

EC ^w\  Co  correspond  to  Fig,  l;  draw  JEi^aiuir)  .F parallel 
to  C.£7  and  C5;  prolong  .E7C  indefinite;  draw  ."i  H  i>eriiendicular 
to  jE7C prolonged.  Draw  the  diagonal  CF,  cutting  (he  chord  line 
of  rail  at  3;  draw  the  chord  E  5;  5  3  shuws  the  amount  {9/')  of 
straight  wood  required  to  point  of  the  mitca"  from  the  verge  of 
cap. 

Fig.  4.  Shouts  the  elevation  of  tan<jcnls  and  how  to  find 
the  bevels:. 

Let  XX  indicate  the  edge  of  drawing  board.  Make  A.B. 
BC.  each  ecinal  EC  and  C  .'">,  on  plan,  Fig.  o.  Perpendicular  to 
XX,  draw  AD,  BE  and  CF  indefinite.  Now  elevate  No.s.  1,  3 
and  3  risers,  making  the  face  of  No.  3  rise  6^'' from  the  spring 
line  AD;  through  the  center  of  balusters  O,  0,  draw  the  under 
side  of  rail, 

>  Parallel  to  the  under  side  of  rail,  draw  the  inclination  for  the 
center  of  rail  indefinite,  cutting  AD  and  BE,  at  D  and  J; 
through  J,  and  i>arallel  with  XX,  draw  KJJj,  intersecting  AD, 
at  K,  and  CF,  at  N:  then  KD  is  the  height  of  the  wreath-piece. 
JD  is  the  increased  length  of  tangent  EC,  on  plan;  JN  i^  a  level 
tangent,  aud  remains  the  same  length  as  C  5,  on  plan.     Make 


Plate  37.  167 

Kb.  equal  CF,  Fig.  3.  Now  make  K  4  equal  the  chord  JEo,  Fig. 
3.  Also  make  J  5  equal  CH,  ou  plan.  Fig.  3.  From  5,  and  per- 
pendicular to  DJ"  produced,  draw  5  6. 

Bevels.  Parallel  with  XX,  draw  the  gauge  line  PQ;  per- 
pendicular to  XX,  draw  QR  equal  to  H  5,  Fig.  3.  Make  QS 
equal  5  6;  also  make  ^P equal  the  height  KD;  draw  RS  and 
RP  produced  to  XX.  lor  convenience  when  adjusting  the  bevel. 

Parallel  with  XX,  draw  the  half  width  of  rail  (2^0.  cutting 
PR  and  SR,  at  8  and  7.  Now  the  bevel  in  the  angle  at  P  is  for 
the  joint  at  miter,  and  the  bevel  in  the  angle  at  iS  is  for  the  shank 
joint,  and  X  8  is  the  increased  width  of  half  the  face-mould  at  the 
miter,  and  X  7  shows  the  increased  width  of  half  the  mould  at  the 
shank.  Make  DG  equal  6^^  for  shank  connecting  the  straight 
rail. 

Fig.  5.     Shows  the  race-mould. 

With  the  steel  square,  draw  the  right  angle  ff  6  5  indefinite. 
Make  6  J  and  6  D,  equal  6  J  and  6  D,  Fig.  4.  With  J  for  a  cen- 
ter, and  C  5,  Fig.  3.  as  a  radius,  draw  arc  cutting  6  5  at  5. 
Draw  J h  prolonged  2^'  to  point  of  miter.  Parallel  v»ith  DJ  and 
J  5,  draw  5  O  and  DO,  for  the  parallelogram  ODJ5,  that  will 
agree,  when  in  position,  with  the  parallelogram  FEC5,  on  plan, 
Fig,  3. 

Proof.  The  chord  D  5,  must  equal  the  distance  D  4,  Fig. 
4,  and  the  diagonal  OJ,  must  equal  the  distance  Dh,  Fig.  4,  if 
so,  the  angle  of  tansents  at  J,  must  be  correct. 

Prolong  JD  6'^  to  G,  for  shank.  Make  joint  at  G  perpen- 
dicular to  GJ\  from  5,  and  at  right  angles  to  J  5,  draw  a  line 
indefinite  to  the  left,  also  prolong  the  diagonal  JO,  to  intersect 
the  line  from  5;  and  from  the  intersection  (not  shown),  draw  a 
line  through  D,  for  the  point  of  contact.  Make  .5  3  and  5  3  eacii 
equal  8  X,  Fig.  4.  Make  G  4  and  G  10  equal  7  X.  Fig.  4.  Draw 
4  8  and  10  9  piiralicl  to  GD;  add  on  2'^  to  point  of  miter  parallel 
to  2  3.  Now  trace  the  concave  side  of  mould  from  9  to  3,  and  for 
the  convex  side  from  8  to  2,  using  a  flexible  strip,  being  careful  to 
tangent  the  straight  lines  at  the  points  2,  3  and  8.  9. 

If  it  be  desirable  to  find  another  point  in  each  curve  as  1  and 
7,  on  the  diagonal,  then  proceed  as  directed  *  for  Fig.  4,  Plate  24. 

Pig.  6.  Shows  the  plan  of  an  S^^  cylinder,  a<jrccuhlc  to 
Fi'j.  2,  Plate  3-1. 

The  balusters  are  2^'  by  2^',  making  the  radius  for  the  center 
line  of  rail  equal  4%''. 

Draw  A  j'and  OC  indefinite  and  at  right  angles;  then  with 
0  as  a  center  and  4^4^''  for  a  radius,  draw  the  semi-circle  ACF; 
from  A  and  F  draw  the  direction  of  straigl'.t  string  to  the  right. 

Now  show  the  graduating  winders  outside  the  spring  of  cyl- 
inder. The  face  of  Nos.  10  and  14  rise  is  l^^'^  from  the  spring 
of  cylinder;  Nos.  9  and  15  rise  is  3>2"'  more,  and  Nos.  8  and  l(j 

*Mr.  Sccor  in  his  work  on  ILnnd-rallinfr  has  fully  described  this 
method  for  finding  the  points  on  the  diazonal  from  tlio  plan.  Also 
Mr.  .James  U.  Monckton,  In  his  1S78  edition  on  slalr-huilding,  has  de- 
scribed the  points  correctl.v  o>i  tlic  diasonal  from  the  plan.  Others 
bav-o  shown  a  center  point  on  the  diagonal,  but  not  correct  in  all 
cases. 

At  sections  L  and  JV  the  dotted  line  Indicates  the  center  of  plank ; 
the  tangent  line  is  carried  across  the  section  .square  to  the  face  of 
crook,  and  intersects  the  dotted  line;  then  tbrouRh  Die  intersection 
the  bevel  is  shown  appliod  from  the  face  of  crook.  The  block  pat- 
tern Is  applied  at  right  angles  to  tlie  line  made  from  bevel;  the  shaded 
p.-vrt  indicates  the  thickness  of  plank  required.  Observe  the  bevels 
do  not  cross  the  tangents  in  their  application. 


168  Plate  37. 

rise  are  each  i}4^^  still  further  out  from  the  spring  line  AF  of 
cylinder  to  the  commencement  of  the  regular  treads  (9^^). 

Next  draw  the  tangents  AB.  BC.  CD  and  DF,  forming  the 
two  square  parallelograms  OCBA  and  OCDF  on  plan  Fig.  6. 

Fig.  7.  Shows  the  elevation  of  tangents  and  the  treads 
and  risers,  ivhich  are  unfolded  from  plan  Fig.  6. 

In  a  case  of  this  kind,  it  will  be  more  economical  to  find  the 
average  pitch  of  the  tangents;  then  the  drawing  may  be  made  on 
a  board  not  over  24^^  wide  and  9'  0^^  long.  Thus,  add  together 
the  width  of  treads  on  the  center  line  of  rail,  and  aroun.d  on  the 
tangeiits,  including  Xos.  7  and  16  treads.  First,  from  the  face  of 
No.  7  rise  to  joint  ot  cylinder  (9^^+5^^+4'^HM^'=183i^O>  equals 
18K''''  plus  4M^^  for  the  tangent  AB;  the  opposite  side  will  equal 
the  same,  'Zo}i^\  Then  the  two  tangents  JSCand  CD  will  equal 
9K^^  more.  The  sum  total  (•2aii^^+23K^^+9K^'=50^0  wiil 
equal  56'^,  which  being  divided  by  10  risers,  equals  5%^^  nearly 
lor  the  average  tread.  The  rise  is  8'''';  therefore  the  average  pitch 
will  be  8^^  by  ^%'\  Now  let  XX  indicate  the  edge  of  drawing 
board;  then  apply  the  steel  square  to  the  edge  of  board,  with  8'''' 
on  the  tongue  and  b]4^^  on  the  blade;  the  tongue  will  give  the 
pitch  FL  for  all  the  vertical  lines. 

Now  set  a  bevel  from  the  edge  of  ])oard  to  Hie  line  FL,  as 
shown,  and  draw  the  perpendiculars  DK,  CJ.  BH a.iv\  AG,  par- 
allel ioF  L  and  equal  to  AB,  BC,  CD  and  DF,  {iK^')  Fig.  6. 

Next  elevate  the  treads  and  risers,  measured  from  the  center 
line  of  rail  on  plan  Fig.  G,  keeping  No.  10  rise  }4^^  from  the 
spring  of  cylinder  AG,  and  No.  14  rise  J^''^from  the  spring  FL; 
No.  9  tread  measures  4^^,  and  No.  S  tread  is  5^';  No.  7  tread  equals 
9^''  wide;  the  measurement  on  the  opposite  side  is  the  same  on 
tlie  ceuter  line  of  rail. 

Through  the  center  of  balusters  O,  0  draw  the  inclination  for 
the  underside  of  rail;  parallel  witli  O,  O  and  O,  0  draw  the  ceuter 
of  rail  to  intersect  AG  at  M,  and  FL  at  N. 

The  next  is  to  give  the  inclination  of  tangents  over  the 
winders.  This  requires  tlie  best  judgment  of  the  stair-builder. 
By  referring  to  Fig.  1,  I'late  34,  observe  the  direction  of  Nos-  9. 
10  and  11  risers,  they  fall  back  froui  the  rail,  while  at  Nos,  13, 
14  and  15  rise,  they  come  out  towards  the  rail.  Or,  in  other 
words,  when  going  up  the  stairs  at  No.  10  step,  the  person  will 
bo  beyond  the  rail,  and  consequently  the  rail  will  feel  high,  and 
when  coming  down  the  stairs  at  No.  14  rise,  the  person  will  be 
forward  of  the  rail,  and  the  rail  if  set  at  the  regular  height  would 
be  too  low.  To  obviate  this,  tlie  rail  must  be  ''lifted"  over  the 
winders  at  Nos.  13,  14  and  15  treads,  and  kept  down  to  about  the 
regular  height  or  less  on  Nos.  8.  9  and  10  winders. 

If  by  lilting  the  rail,  it  .should  come  a  little  high,  that  will  be 
a  good  fault,  but  if  the  stair-builder  should  miss  it,  and  the  rail 
be  low,  then  the  owner  would  lind  fault,  as  then  there  would  be 
danger  when  going  down  the  stairs. 

The  worst  diflicuUy  the  stair-builder  will  have,  and  where  his 
best  judgment  will  be  required  in  lifting  the  rail,  will  be  over 
Nos.  13,  14  and  15  treads.  At  Nos.  8,  9,  10  and  11  treads,  there 
will  be  no  danger,  as  the  direction  of  risers  fall  back  of  the  rail, 
and  the  rail  will  naturally  apjjcar  high  even  when  kept  a  little 
below  tliu  height  of  a  regular  short  baluster. 

If  th«!  risers  in  the  cylinder  were  to  radiate  from  the  center 
O,  then  tlie  difficulty  of  regulating  the  lieight  of  tangents  in  the 
cylinder  would  be  obviated,  as  the  person  would  then  be  normal 
to  the  curve  in  the  direction  of  any  of  the  treads,  but  it  is  only 
where  there  is  ample  room  that  the  winders  can  be  so  placed. 


Plate  37.  169 

At  Fig.  1,  Plate  34,  the  diameter  line  is  extended  to  the 
walking  line,  and  happens  to  cut  the  walking  line  at  Nos.  9  and 
15  rise.  Now  let  it  be  observed  that  the  diameter  line  being 
extended  cuts  across  Nos.  10  and  14  rise,  thus  indicating  that  the 
point  on  the  walking  line  at  No.  9  rise,  is  one  rise  lower  than  at 
the  joint  of  cylii.der.  At  the  opposite  side  the  joint  of  cylinder 
will  be  two  risers  lower  than  at  the  point  of  intersection  with  the 
walking  line,  consequently  we  will  have  to  lift  the  tangent  at  the 
angle  D,  on  plan,  say  nearly  two  risers. 

Then  set  up  from  No.  13  tread  to  It  \^",  and  from 
any  point,  say  Q,  on  the  line  JPiV,  draw  the  inclination 
lor  the  upper  laugcnt,  cutting  the  perpendiculars  FL,  and  DK, 
at  JL  and  I,  and  intersecting  CJ  at  S.  From  I,  draw  the  incli- 
i:alion  of  tangents  to  touch  the  arc  at  T,  and  cut  the  perpendic- 
ulars JC,  HB  and  GA,  at  Z7,  H  and  W,  and  prolonged  to 
inlerstct  MB  at  y.  Perpendicular  to  FL  draw  LJ  and  UF, 
cutling  DK  at  2  and  o.  At  right  angles  to  AG,  draw  WC, 
cutting  BH  at  4;  tlicn  CU  will  be  the  height  of  the  lower 
wri-ath-picce,  and  FL  will  be  the  height  of  the  upper  wreath- 
piece.  ( 

Prolong  HI  to  intersect  iJ^at  V;  from  3,  and  at  right  angles 
to  VU,  draw  3  5;  from  ;3,  and  at  right  angles  to  LS,  draw  2  19; 
from  4,  and  at  right  angles  to  HW,  draw  4  6.  Make  C  22  and 
U  18  eacli  equal  the  chord  AC,  on  plan.  Fig.  6.  Parallel  witli 
DK.  draw  the  half  width  of  rail  (2^0.  intersecting  IL  and  UI, 
at  20  and  21.  At  W,  allow  4^^  and  at  L,  allov/  2'^  for  shank. 
Ease  the  angles  at  y  and  Q,  to  please  the  eye.  Opposite  the  face 
of  Nos.  8  and  10  rise,  draw  the  face  of  rise  to  intereect  the  center 
of  rail  at  00  and  00,  for  points  to  raeasui'e  from  when  jointing 
the  straight  rail.  These  points  should  be  marked  on  the  patterns, 
also  the  distance  M,  00  (12}-r;^^),  and  N,  00  {V2y/'),  to  be  con- 
venient when  jointing  the  straight  rail. 

Bevels.  aa  indicate  the  edge  of  drawing  board,  and  the 
doited  line  indicates  a  gauge  lin(!  parallel  with  aa/  ix'ipendicular 
to  aa,  draw  bf,  ecjual  to  OC,  on  plan,  Fig.  0.  Make  bh  equal 
2  It);  also  make  bm  equal  5  3;  let  bn  equal  4  G;  draw  fm,  fn 
and  fli  prolonged  to  the  edge  of  board. 

Now  in  the  angle  at  h  is  found  the  bevel  for  the  shank  joint 
24,  and  in  the  angle  at  m  is  found  the  bevel  for  the  joint  at  Z7on 
tiie  upper  wreath-piece.  As  the  tangents  UH  and  HW  are  of 
the  same  length,  only  one  bevel  will  be  required  at  the  lower 
wreatli-piece.  The  angle  at  72  gives  the  bevel  for  both  joints  of 
the  lower  wreath-piece. 

Fig.  8.     Shoivs  the  face  mould  for  the  loivcr  wreath-jnccc. 

Draw  BAFio  equal  HWT.  Fig.  7;  with  A  for  a  center  and 
U  22,  Fig.  7,  as  a  radius,  draw  arc  at  C;  then  with  B  for  a  cen- 
ter and  BA  as  a  radius,  draw  arc  intersecting  at  C,  join  BC 
parallel  witli  AB  r.nd  CB;  draw  CO  and  AO  prolonged. 

Priinf.  03  must  equal  the  diagonal  OD,  Fig.  G;  if  so,  the 
angle  of  tangents  at  B  must  be  correct. 

Make  A  2,  A  S  and  C  4,  C5  each  equal  J 21,  Fig.  7:  make 
OD  equal  the  radius  li%^^)  of  the  center  line  of  rail;  let  D  G  and 
D  7  each  equal  the  half  width  of  rail  (2^0- 

Make  joints  at  C  and  .F' perpcuidicular  to  tangents  SJ*  and 
BC;  parallel  with  BF  draw  2  8  and  3  9  lor  the  shank;  now 
pivot  the  trannnel  at  O  at  right  angles  to  BO,  and  set  from  pencil 
to  minor  pin  the  distance  OD  lor  the  center  or  fdVinij  line  of 
rail;  then  place  the  pencil  in  C,  and  drop  the  pins  in  the  grooves, 
g 


170  Plate  37. 

and  fasten  the  major  pin;  then  trace  the  curve  CD  A;  repeat  the 
operation  lor  the  concave  and  convex  side  of  mould.  The  bevels 
are  shovtii  applied  through  the  center  of  plank  at  sections  L  and 
N;  the  )>evel  at  L  is  applied  so  as  to  elevate  the  joint  at  C,  and 
at  iVthe  bevel  is  applied  so  as  to  pitch  the  joint  at  i^dowu. 

Fig.  0.    Shows  the  face-mould  for  the  upper  irrcdth-piecc. 

The  tangents  being  of  unequal  length,  there  will  be  two 
bevels  required,  as  the  shortest  tangent  connects  with  the  easing 
at  the  upper  end,  the  steepest  bevel  will  apply  to  that  joint.* 
Draw  CB  equal  to  tangent  JZ7,  Fig,  7.  With  C  as  a  center  and 
J  18,  Fig,  7,  for  a  radius,  draw  arc  at  A;  with  .B  as  a  center  an<l 
tangent  IL  for  a  radius,  draw  arc  intersecting  at  A;  join  SA 
lirolonged  to  H,  equal  to  I  24,  Fig.  7.  Parallel  with  CB  and 
BA  draw  AO  and  CO,  for  the  parallelogram  OABC,  on  the  cut- 
ting plane. 

Proof.  The  diagonal  BO  must  equal  iS  18,  Fig.  7;  make  CD 
equal  IV,  Fig.  7;  di'aw  DO  produced;  let  Oi^  equal  the  radius 
OC,  Fig.  G;  make  FO  and  F  7  each  eijual  the  half  width  of  rail 
(:i'0;  uiake  A  2  and  A  3  each  equal  1-21,  Fig,  7.  Make  Cl  and 
C  5  each  equal  I  20,  Fig.  7;  make  joints  at  C  and  Hut  right 
angles  to  the  tangents  CB  and  BH;  draw  2  8  parallel  with  BH 
for  the  shank  on  the  concave  side.  On  the  convex  side  the  joint  in- 
tersects the  curve. 

Now  pivot  the  trammel  at  O,  with  the  arms  resting  perpen- 
dicular to  the  semi-minor  axis  OF,  and  trace  the  inside  and  out- 
side curves  of  face-mould  in  the  same  manner  as  has  been  ex- 
plained. Tha  letters  JP  and  Q  show  the  sections  of  the  joints  H 
and  C;  the  bevels  are  applied  through  the  center  of  plank.  The 
bevel  at  Q,  let  it  be  observed,  is  applied  so  as  to  throw  the  shank 
end  up,  v.hile  at  the  shank  end  the  bevel  is  applied  so  as  to  throw 
the  center  joint  at  C  down. 

Fig.  10.  Shows  the  plan  of  the  center  line  of  rail  for  t)ic 
cyluifler,  stmting  in  the  second  story.      See  Fig.  7,  Plate  31. 

Make  Ai?  equal  the  diameter  (0'.<''^)  for  the  cent' r  line  of 
rail,  with  O  as  a  center;  draw  the  semi-circle  ACE:  enclose  the 
semi-circle  with  the  tangents  AB,  BC,  CD  and  DE;  prolong 
DE  and  BA  indefinite  to  the  left.  Tlie  face  and  directions  of 
risers  are  made  to  agree  with  Fig.  7,  Plate  34.  Oji  the  center  line 
of  rail  the  face  of  No.  4  rise  is  shown  %^^  from  the  spring  of 
cylinder;  No.  4  tread  measures  4^^  and  No.  5  tread  measures  9''-' 
on  the  center  line  of  rail;  the  regular  pitch  is  8^'  rise  by  9^^  tread. 

Fig.  11.  Shoivs  the  development  of  tangents  atid  the  eleva- 
tion of  treads  and  risers,  measured  from  the  center  line  of  rail 
on  the  line  of  tangents  on  plan,  Fig.  10. 

First  find  the  average  pitch  on  the  center  line  from  E, 
around  the  tangents  to  No.  (>  rise  from  plan.  Fig.  10.  From  the 
face  of  No.  6  rise  to  B  equals  1S}4^'';  from  B  to  D  equals  {)}.<^^, 
and  from  D  to  E  e(iuals  4K^^  total  (18};r^^^-93-2^^'^-4%^^=33'0 
equals  o-J^'',  which  being  divided  by  G  risers,  equals  5X'''  for  tlie 
average  tread.  Then  with  the  square,  take  532^^  on  the  blade 
and  the  rise  (8^^)  on  the  tongue,  and  apply  to  the  edge  of  l)oard 
XX;  the  tongue  will  give  the  line  AJ  required  for  the  average 
jiitcli  iioni  the  edge  of  drawing  board.  Parallel  witli  AJ,  draw 
BK,  CH,  DG  and  E,  equal  to  AB,  BC  CD  and  DE,  on  plan, 
Fitj;.  10.  (t5:Ceach).  Now  draw  the  floor  line  Z/i,  at  right  an- 
gles to  CH.  ,, 

*  It  is  well  to  note  this,  as  some  use  a  parallel  f  ace-moulcl. 


Plate  37.  171 

Make  the  position  of  No.  1  rise  from  D,  equal  tliat  on  plan, 
Fig.  10,  {V)\  then  elevate  the  risers  and  treads  from  the  tan- 
gents on  plan,  making  the  risers  parallel  and  the  treads  at  right 
angles  to  the  pcrpeEdicular  lines,  keeping  No.  4  rise  %^^  from 
the  spring  line  AJ;  No.  4  and  No.  5  treads  equal  4'^  and  *y^ 
each.  Now  through  the  center  of  baluster  mm,  draw  the  incli- 
nation for  the  under  side  of  rail.  Parallel  with  m.m.,  draw  the 
center  of  rail  MN;  it  will  be  observed  that  the  regular  pitch 
intersects  the  spring  of  cylinder  at  N.  On  Ihe  plan.  Fig.  3, 
Plate  34,  extend  the  diameter  Uiie  to  cut  the  walking  line  at  A; 
let  it  be  observed  tliat  the  joint  of  cylinder  comes  in  No.  3  tread 
at  C,  and  the  diameter  line  cuts  across  No.  4  rise;  and  will  rest  at 
about  the  center  of  No.  4  tread,  thus  indicating  the  point  A  will 
he  one  rise  and  a  half  above  the  point  C,  on  the  inclination  ot 
rail.  Then  that  is  about  the  height  above  No.  3  tread,  that  tlie  in- 
clination of  the  upper  tangent  should  cross  the  perpendicular 
AJ,  in  the  elevation  say  at  P;  now  allow  fnan  iVto  Q  sufllcient 
to  make  an  easing  on  the  straight  rail  to  connect  the  shank  of 
wreatli-piece. 

Then  from  Q,  through  P.  draw  tangent  cutting  BK  at  O. 
and  prolonged  to  intersect  CiJ  at  i?.  From  the  floor  line  at  L 
set  up  lialf  a  rise  to  the  under  side  of  rail  taken  from  the  first 
flight  (4^^  in  this  case),  and  \W^  more  to  the  center  of  rail, 
making  SM''^  from  the  floor  line  LL  to  the  center  of  rail  at  S. 
I'arallel  to  LL  dvavv  SC,  cutting  DG  at  T:  connect  TO,  cutiing 
CH  at  U.  From  U  and  P,  and  at  right  angles  to  CH,  draw  UA 
and  PiiT.  cutting  BK  ai  V  and  9.  then  CU  will  be  the  height 
fin-  the  lower  vireath-piece,  and  AP  w  ill  be  the  height  for  the 
upper  wreath-] )iece. 

Prolong  Z70  to  intersect  PH  at  Y;  make  U7  and  CS  each 
e(iual  to  the  chord  AC,  on  plan  Fig.  10.  From  9,  and  perpendic- 
ular to  Pi?  produced,  draw  9  10;  from  Vand  at  right  angles  to 
UY,  draw  V  12;  at  O  draw  the  half  widtli  of  rail  (2^^)  parallel 
with  BK,  cutting  PR  at  13  and  OU at  14. 

Bevels.  Parallel  with  LL  draw  the  dotted  line  WIS:  per- 
])i'ndicular  to  LL  draw  WZ,  equal  to  the  radius  OC,  Fig.  10; 
nr.ike  W  16  equal  V  12,  an^d  Wl7  equal  to  9  10;  niake  W  18 
equal  tlie  height  CU;  draw  Z  IS,  Z  17  and  Z  IG  prolonged  to  LL, 
for  the  bevels  required. 

Fig.  12.     Shines  the  facc-mmi.ld  at  the  starting. 

Draw  the  rectilineal  parallelogram  OEDC.  making  EO  and 
DC,  a!.so  OC  and  ED  enr-h  equal  UT  and  TC,  Fig.  11. 

Proof.  The  chord  EC  and  the  diagonal  OD  must  each  equal 
Z78,  Fig.  11.     If  so,  the  parallelogram  is  correct. 

Make  E  2  and  iJ7  3  each  equal  O  14,  Fig.  11.  Let  C4  and 
C .')  each  ecpial  the  half  width  of  rail  (2^^).  Pivot  the  Iranimel 
in  O,  with  the  arms  centered  on  the  semi  major  axis  OE,  and 
trace  the  concave  and  convex  sides  of  face-mould,  as  has  hvx  n 
described;  add  on  2^''  or  more  straight  wood  at  ^parallel  to  OE, 
to  help  the  easing  at  the  joint  connecting  the  straight  rail.  The 
minor  axis  OC  forms  the  joint  at  C.  The  section  at  JV" shows  Ihe 
bevel  found  in  the  angle  at  IS.  Fig.  11,  ajiplied  so  as  to  pilch  tlie 
joint  at  Cup,  and  at  section  iWthe  square  is  shown  applied  from 
the  face  of  crook,  allowing  the  tangent  ED  to  be  horizontal. 

Fig.  13.  Shows  the  face-mould  for  the  upper  torcath- 
plccc,  connrotinr;  the  casement,  Fiij.  11. 

Make  CB  equal  tangent  OU,  Fig.  11,  With  C  as  a  center 
and  7  H,  Fig.  11,  for  a  radius,  draw  arc  at  A;  with  J3  as  a 


173  Plate  37. 

center,  and  tangent  OP,  Fig"  11,  for  a  radius,  draw  arc  intersect- 
ing at  A;  join  BA  and  produced;  draw  AO  and  CO  parallel 
with  BC  and  BA  prolonged,  for  the  parallelogram  OABC  on 
the  cutting  iilane. 

Proof.  The  diagonal  BO  must  equal  the  distance  i?  7,  Fig. 
11.     If  so,  the  angle  of  tangents  at  B  is  correct. 

Make  AE  equal  P  19,  Fig.  11;  make  joints  at  E  and  C 
at  right  angles  to  tangents  BE  and  BC;  make  A  ii  and  A  o 
each  equal  O  14,  Fig.  11;  also  make  C  4  and  C5  each  eiiual  O 
13,  Fig.  11.  Let  CF  equal  OY,  Fig.  11;  join  OF,  and  pro- 
longed, for  the  direction  of  m.inor  axis;  make  O J" equal  to  radius 
OC,  on  plan  Fig.  10.  Make  J 6  and  J 7  each  equal  the  half 
width  of  rail  (2^0;  draw  the  shank  2  8  parallel  with  BA. 

Pivot  the  trammel  at  O  with  the  arms  at  right  angles  to  the 
somi-minor  axis  OJ,  and  set  from  pencil  to  minor  pin  the  distance 
OJf  for  the  ceiiter  line  of  rail;  then  place  the  pencil  in  A, 
and  slide  the  major  pin  until  they  both  drop  into  the  grooves, 
then  fasten  the  major  pin  and  trace  the  center  or  fnlUn(j  line; 
pioceed  in  the  same  manner  to  trace  the  concave  and  convex 
bides  of  face-mould. 

At  D  and  P,  the  sections  show  the  bevels  applied  through 
the  center  of  plank;  the  bevel  found  in  the  angle  at  17,  is 
applied  at  JD,  and  the  bevel  found  in  tlie  angle  at  16,  Fig.  11,  is 
applied  at  P,  alwa3-s  from  the  face  or  upper  side  of  crook, 
which  must  be  true,  or  out  of  wind. 

Fig.  14.  Shows  plan  of  the  center  line  of  rail  for  the 
quarter  ijace  winding  landlncj  in  tlw  third  story. 

The  diameter  of  cylinder  is  8^^,  and  the  radius  for  the 
center  line  of  rail  is  ■i^i^''. 

Make  AE  equal  OV,^^;  v^itli  a  radius  of  4^^^^  and  O  for  a 
center,  draw  tlie  srmi-circle  ACE,  for  the  center  of  rail.  Draw 
the  rectilineal  paral!eloo;vam  ABDE,  tangent  to  the  curve  at 
the  points  A,  C  and  E;  prolong  BA  and  DE  for  the  direction 
of  straight  rail. 

In  practice  for  a  working  drawing,  the  direction  of  winders 
and  flyers  showing  how  oblique  they  cut  the  string  line,  are 
supposed  to  be  laid  out  on  paper  full  size  from  the  scale  drawing. 
Fig.  3,  Plate  34.  The  plan  shows  No.  11  tread  measiires  4^^ 
on  the  center  line,  and  No.  12  rise  Ji^^  from  joint  or  spring  of 
cylinder. 

Fig.  15.  Shows  the  devchypmcnt  of  tangcuts  and  tlie 
elevation  of  treads  and  risers  measured  frcmi  the  tangents 
and  straight  part  on  plan,  Fig.  11. 

For  convenience,  first  find  the  average  tread  from  the  face  of 
No.  10  rise,  around  the  tangents  to  face  of  No.  1.')  rise;  thus 
from  No.  10  rise  to  spring  of  cylinder  ('J'^+4'''^  Ji^^=13^X^^) 
e(iuals  133i^^,  pl^^i  AB,  (4M^0'  I'l"^  ±'''"»i  -^  *<>  f'i<-'«  of  No.  l.'i 
rise  (SK'O.  equals  (13M^^-f-4%^'+83.<'^=-27^0  l'<>i"  tlie  total  27^^ 
which  behig  divided  by  5  risers  (27^^H-.5=53id^^)  equals  5>'s^^ 
nearly  for  the  average  tread. 

Let  XX  indicate  the  edge  of  board;  then  with  b^'^  on  the 
blade,  and  b"  on  the  tongue,  draw  the  direction  of  the  perp-^i- 
dicular  EF  from  the  tongue.  Parallel  with  EF,  draw  DG,  CH, 
SJ'and  AK  indelinife. 

Now  elevate  Nos.  10,  11,  12,  13,  14  and  1.5  risers  and  treads, 
keeping  No.  12  rise  %^'  from  the  spring  line  AK,  as  shown. 
Draw  the  floor  line  at  the  lauding;  from  the  floor  line  set  up  4^'' 


Plate  37.  1T3 

to  under  side  of  rail,  aud  IH^^  more,  or  BH^^  to  the  eentor 
nf  rail  at  L,  At  right  angles  to  EF,  draw  LN,  cutting  EF  at 
F,  and  DG  at  N. 

Through  the  center  of  balusters  O,  O,  draw  the  under  side 
of  rail;  parallel  with  00;  draw  the  ceuter  of  rail  FM,  inter- 
secting AK  at  M;  draw  arc  equal  to  the  half  thickness  of  rail 
at  the  center  of  baluster  No.  12  tread,  then  from  the  point  N, 
draw  a  line  tangent  to  the  arc,  intersecting  the  inclination  MP  at 
Q,  and  cutting  the  perpendiculars  CH,  BJ  and  AK,  at  R,  y 
and  iS. 

From  S,  and  at  right  angles  to  AK,  draw  /SC,  cutting  JB  at 
T;  from  B,  and  perpendicular  to  CH,  draw  RTJ,  cutting  GB  at 
Y;  then  TJF  is  the  height  for  the  upper  wreath-piece,  and  RC 
is  the  height  for  the  lower  wreath-piece;  and  NR,  Rj  and  jS 
show  the  increased  length  of  tangents  in  elevation;  make  joint  at 
W  at  right  angles  to  QS;  ease  off  the  angle  at  Q  to  please  the 
eye,  and  to  tangent  the  joint  at  W;  make  JJ  2  and  C  3,  each 
equal  the  chord  CB,  on  plan.  Fig.  14.  Parallel  with  DG, 
draw  the  half  width  of  rail,  cutting  the  tangent  NR  at  4:  from 
T,  and  at  right  angles  to  JR/S,  draw  TS. 

Bevels.  As  the  tangent  FN  is  level,  there  will  be  but  one 
bevel  for  the  landing  wreath-piece,  and  as  both  tangents  Rj  and 
yS,  for  the  lower  wreath-piece,  have  the  same  inclination,  there 
will  be  but  one  bevel  required  for  both  joints.  Let  aa  indicate 
the  edge  of  board,  and  the  dotted  line  be  a  gauge  line  parallel  to 
aa;  draw  6  7  perpendicular  to  aa,  and  equal  to  OC,  on  plan, 
Fig.  14;  make  6  8  equal  T  5,  aud  6  9  equal  the  height  TJF; 
draw  7  8  and  7  9  produced,  to  edge  of  board  aa  for  the  bevels  iu 
the  angles  at  8  and  9. 

Fig.  16.    Shoivs  the  fncc-mould  for  the  quadrant  ACO, 

Fiq,  14. 

Make  WAB  equal  WSY,  Fig.  15.  With  A  as  a  center, 
and  R,  3.  Fig.  15,  for  a  radius,  draw  arc  at  C,  again  with  B  as  a 
center  and  AB  as  a  radius,  draw  arc  intersecting  at  C;  with  the 
same  radius  and  C,  also  A,  as  centers,  draw  arcs  intersecting 
at  0;  draw  OA  and  OC  indefinite,  and  we  have  the  parallelo- 
gram OABC  on  the  cutting  plane,  that  will  agree  with  the  par- 
allelogram OABC,  on  Plan  Fig.  14,  whtn  in  position. 

Proof.  The  diagonal  OB  must  ecjual  the  diagonal  OB,  on 
plan  Fig.  14.  Draw  BO  indefinite  for  the  direction  of  minor 
axis.  Make  OD  e.iuai  OC,  on  plan  Fig.  14;  make  A  2,  AS,  C4 
and  C  5  each  equal  N  i.  Fig.  15.  Let  D  6  and  D  7  eaoh  equal  the 
half  width  of  rail  (2").  Make  joints  at  C  and  W  at  right 
angles  to  the  tangents  BA  and  BC.  Parallel  with  B  Wdraw  2  8 
for  the  shank.  Kow  pivot  the  trammel  at  O,  with  the  arms  at 
right  angles  to  the  semi-minor  axis  OD,  Set  from  pencil  to  minor 
pin  the  distance  OD;  then  rest  the  pencil  in  C,  drop  the  pins  in 
the  grooves.  Now  fasten  the  major  pin,  aud  trace  the  center 
curve  of  face-mould.  Proceed  in  the  same  manner  to  trace  the 
concave  and  convex  sides  of  moidd. 

The  sections  G  and  H  show  the  application  of  the  joint  bevel, 
which  is  taken  from  the  angle  at  8,  Fig.  15. 

Fig.  17.  Shov:s  the  facc-mouhl  for  the  quadrant  OEC, 
Fifj.  14. 

Diaw  tlie  rectilineal  parallelogram  OCDE,  making  OC  and 
BE,  also  OE  and  CD,  to  equal  FN  and  NR,  Fig.  15,  respect- 
ively. 

Proof.     The  diagonals  OD  and  EC  must  equal  F2,  Fig.  15. 

Make  C  2  and  C  3  each  equal  the  half  width  of  rail  (2^0 ;  let 


174  Plate  37. 

E  4:  and  J575  each  equal  Na,  F.ig.  15.  Now  pivot  the  trammel  at 
O,  with  the  anus  resting  on  the  semi-major  axis  OS.  Then  set 
I'rom  pencil  to  minor  pin,  equal  to  OC,  and  trom  pencil  to  major 
pin  to  equal  OE.  Xow  trace  tlie  center  line  on  face- mould  from 
^to  C;  proceed  in  lilve  manner  to  trace  the  concave  side  of  face- 
mould  tlirougli  tlie  points  4,  2,  and  convex  side  throngli  the  points 
5,  3.  Parallel  with  4  5  add  2^^  of  straight  wood  EF.  to  help  the 
easing  in  wreath-piece,  to  connect  the  straiglit  rail  LF,  Fig.  15. 
The  bevel  at  section  M  is  taken  from  the  angle  at  9,  Fig.  15, 
aiul  applied  from  the  face  and  through  the  center  of  plank,  so  as 
to  pitch  the  joint  at  C  down.  At  section  iVthe  block  pattern  is 
applied  parallel  to  the  face  of  crook,  and  at  the  center  of  plank. 

Fig.  18.  Shoivs  the  caacmcnt  required  at  the  Inndinfj  of 
the  Jirst  flhjht. 

Through  the  center  of  balusters  G,  O  draw  the  underside  of 
rail  parallel  with  O,  0;  draw  the  center  of  rail  AB  indefinite. 
From  the  floor  line  set  up  4'^  to  underside  of  rail,  and  1}4^^  more 
to  C  for  center  ofjrail  (4"— IK^^^^oK^O.  equals  5^^^.  Parallel 
with  floor  line  draw  CB,  intersecting  AJ3  at  B.  Now  ease  off  the 
angle  ABC,  to  please  the  eye;  plumb  over  the  face  of  No.  17  rise; 
make  a  point  D,  showing  the  face  of  landing  rise  No.  17  on  the 
easement  pattern.  Now  marlc  on  the  pattern  the  distance  (14^^^) 
from  D  to  join  C,  for  the  amount  to  allow  for  easement  when 
joiuting  the  straight  rail. 

Jointing  the  rail.  No.  l  length.  -The  leno-th  from  th 
-pring  of  turnout  to  spring  of  cylinder  equals  G''  S^^  Fig.  2,  Plate 
:'4;  the  length  of  shank  on  face-mould,  Fig.  5,  equals  6'^  and  the 
distance,  M,  00,  Fig,  7,  equals  I2y/^,  and  from  00  to  joint  at  E 
equals  V  Z",  or  2''  ^\i"  from  M  to  joint  at  E,  as  the  allowance 
for  ramp.     Then  the  dimension  to  cut  No.  1  length  (G''  8'''' — (2'' 

"No.  2  length.  From  joint  of  cylinder  to  face  of  No.  17  rise 
landing  equals  ?J  V,  Fig.  2,  Plate  34.  The  easement  connecting 
the  wreath-piece  at  the  upper  end  measures  from  iVto  00  12)^''^; 
then  2M/'  minus  12K^^  C^^  1^^— 1^  0K'^=1^  0}4''),  equals  1^ 
OK'''',  as  the  distance  between  tiie  two  points  00,  Fig.  7,  and  tlie 
point  D,  Fig.  18.  This  will  allow  QH'^  from  D  to  joint  at  A, 
Fig.  18,  and  &li'^  from  00  to  joint  near  P,  Fig.  7.  as  shown. 

JVo.  5  length.  The  length  from  face  of  No.  17  rise  to  spring 
of  cylinder  starting  second  flight  equals  3''  0'^  Now  the  hori- 
zontal distance  from  D  to  C,  Fig.  IS,  equals  14^^^  for  the  level 
length  on  easement  landing  of  the  first  flight,  and  we  have  2,"  of 
straight  wood,  EB,  added  on  to  the  lower  end  of  wreath-piece, 
Fig.  12  (143^ ^^+2^^:=!^  4K''0.  which  equals  V  ^Y,"  to  be  de- 
ducted from  the  wJiole  length  (3'9'^— 1'  4K''^^2^  4K^0.  equals  2' 
4K^^,  the  length  to  cut  No.  3. 

iVo.  4  Length.  The  length  from  spring  of  cylinder  starting 
to  spring  of  cylinder  landing  in  the  second  flight  equals  7^  OM^', 
see  Fig.  4.  Plate  34.  The  length  of  easement.  Fie.  11,  measures 
from  t.pring  of  cylinder  at  iVto  Q,  G'^,  and  from  Q  to  joint  at  M, 
9K'^;  (G'^+9K^^=15X'0  equals  15K^'  to  allow  for  the  easement; 
and  for  the  ramp.  Fig.  15,  allow  G'^  from  M  to  the  point  plumb 
over  the  face  of  No.  11  rise,  and  lihi^^  more  to  the  lower  joint  of 
ramp  at  P,  which  being  added  (14K'^--6'^=1'  SK''^).  equals  V 
8X^^  plus  the  length  of  easing  al)ove'(15K'0  [1.8>2+1'  3K''=3' 

*  Note.— The  face  of  second  lise  is  mostly  taken  as  a  fixed  point 
from  which  to  measure  for  the  first  lensrth  in  straight  flights;  in  this 
case  we  have  taken  the  measure  from  the  spring  of  turnout. 


Plate  37.  175 

8''],  equals  3'  0'^  to  be  deducted  from  7^  0%'^  (7^  0%^'— 3^  0'' 
=4'  OM^O.  equals  4^  0%-",  the  leugth  to  cut  JNo.  4. 

JV'o.  5  Icnrjth.  Is  the  second  level,  and  is  marked  6^  7^'  from 
spring  of  cj'Jinder  landing  in  the  third  story  to  the  spring  of 
quarter  cylinder.  Now  we  have  allowed  2^^  of  straight  wood 
FE,  on  face-mould,  Fig.  17;  then  deduct  2'^  from  the  whole 
length,  6^  7^^,  equals  6^  5'^  to  cut  No.  5  length.  In  case  there  be 
straight  wood  on  the  quarter  turn,  deduct  the  amount  of  straight 
wood  in  addition  to  the  2^^  allowed  on  the  wreath-piece. 

The  short  piece  to  wall  equals  3^  0^^  in  length.  After  the 
joints  are  made,  bolted  and  dressed  off,  the  rail  is  ready  to  hang. 

IIwGiNG  THE  Eail.  In  large  stair  shops  it  is  customary  for 
one  set  of  men  to  step  up,  and  another  to  hanj;  rails  and  complete 
the  job,  while  neither  get  them  out.  So  a  few  words  in  addition 
to  what  has  been  said  for  a  platform  stair-case,  will  not  be  out  of 
place  here. 

When  proceeding  to  hang  the  rail  over  winders,  as  in  this  case, 
a  very  good  plan  is  to  elevate  the  rail  on  stanchions  notched  out  to 
receive  the  rail.  Let  the  rail  be  raised  or  lowered  to  suit  the  height 
of  the  regular  balusters,  and  plumb  carefully  on  the  convex  side 
to  points  made  at  intervals  on  tlie  steps  and  around  the  cylinder. 
The  distance  in  to  mark  the  points  from  the  face  of  bracket  line 
equals  half  the  thickness  of  balusters  (1")  plus  the  half  width  of  rail 
('2"),  equals  3"  for  the  convex  side  of  rail.  Now  when  the  rail  is  plumb 
to  the  points  around  the  cylinder  and  the  straight  part,  and  also  the 
height  to  suit  the  baluster  is  correct,  then  plumb  through  the  center 
of  cap  for  the  center  of  newel  on  the  floor,  and  take  the  height 
from  floor  to  under  side  of  cap  for  the  height  of  newel.  The 
newel  may  now  be  cut,  set,  and  the  rail  placed  in  position,  using 
stanchions  for  supports,  set  near  the  joints  and  out  of  the  way  for 
glueing  and  driving  up  the  nuts. 

Next  if  the  straight  rail  have  any  bends,  they  may  now  be 
straightened  by  l:)racing;  plumb  and  bore  for  the  balusters,  dress  off 
the  under  side  of  rail  and  put  the  balusters  in  place,  using  a  thick 
glue  for  this  purpose. 

After  the  balusters  have  been  set  and  glued  at  intervals,  remove 
the  stancliious  and  complete  glueing  in  the  balusters.  Some  prefer 
to  hang  the  rail  at  once  on  a  few  balusters;  the  stanchions 
make  the  rail  more  solid,  and  may  save  a  broken  twist,  and  is 
better  for  straightening  the  crooked  part  of  straight  rail,  whicli  often 
has  to  be  done. 

If  the  stairs  are  got  out  and  stepped  up  carefully,  the  newel  and 
balusters  may  be  cut  at  the  bench.  It  will  be  noticed  at  Fig.  4,  that 
the  under  side  of  rail  is  drawn  through  the  center  of  baluster, 
and  its  length  is  naught  at  that  point,  while  the  under  .side  of  rail  is 
raised  up  6"  above  the  first  step  to  allow  for  easing  at  the  newel;  then 
whatever  height  from  top  of  step  to  under  side  of  rail,  we  make  the 
short  baluster,  the  newel  will  be  6"  longer  from  the  top  of  first  step 
to  the  under  side  of  rail,  or  from  the  floor  to  under  side  of  rail  will  be 
the  height  of  arise  [8"]  more,  or  14",  in  this  case;  for  instance,  the  height 
of  a  short  baluster  from  the  top  of  the  .step  to  under  side  of 
rail  at  the  center  is  2'  I'J".  and  the  newel  is  fi"  higher  than  a  short  bal- 
uster, plus  the  height  of  first  rise  8",  will  Ofjual  for  the  whole  height 
of  newel  from  the  floor  to  under  side  of  cap  3'  Sli",  (2'  in"  i-C"-rS"= 
3'3;i"). 

For  pin  top  balusters  allow  lY,"  to  enter  the  rail;  the  height  of 
couare  is  half  a  rise  for  the  short  ones,  and  the  length  of  turning 
bein"  all  the  same,  will  make  the  squares  for  the  base  of  long  bal- 
uster equal  the  height  of  a  rise;  sometimes  the  balusters  are 
square  at  the  top  and  also  at  the  base;  the  squares  at  the  base  and 
top  for  both  balustei's  being  the  same  height,  then  the  turning 
for  the  shafts  will  be  the  ditference  of  half  a  rise;  .sometimes  the 
squares  at  the  base  are  one  height  and  the  shafts,  also  one  length  in 
turnino-.  and  the  squares  at  the  top  of  different  lengths. 

To  find  the  length  of  odd  balusters  under  the  wreath  part  of  rail, 
study  Fi"^s.  1  and  2,  Plate  32;  to  prevent  a  confusion  of  lines,  this  is 
omitted  liere,  however,  for  common  work,  if  the  balusters  have 
their  shafts  ail  turned  the  same  length,  the  difference  will  be  in  the 
square  at  the  base,  and  will  not  be  objectionable  unless  the  propor-. 
tion  is  too  much  out  of  the  way.  ^r,       ^   .         ,.       .,. 

Boeing  the  Rail.  This  is  best  done  on  the  .stairs  after  the 
rail  is  hung,  the  plumbing  and  boring  for  the  balusters  is  a  short  job 
for  a  flight  of  stairs;  for  Ijoring  around  the  winders,  use  a  ratchet 
or  angle  brace. 


176  Plate  38. 


PLATE  38, 

Plate  38,  Pigs.  1  and  2.  [Scale  }4^^=1^.\  Exhibits  plan 
elevation  of  a  doithle  qiiaHcr-jxice  winding  stair-case,  having  a 
(inart£r  pace  and  four  risers  to  the  landing  in  the  second  story; 
the  quarter  pace  nt  the  starting  has  a  circidar  ^vall  string,  and 
tke  circidar  corner  is  ornamrrded  with  a  nitch. 

The  heiglit  of  story  is  V.y  C  from  top  to  top  of  joist;  the  joist 
are  10'^  wide  in  the  second  story,  and  they  are  to  be  stripped  across 
for  lath  and  plastering  witli  V  by  3^^  strips,  malving  IV^  for 
tlu;  depth  of  joist.  The  width  of  hall  is  8^  2'^;  the  height  of  door 
under  the  stairs  is  7^  C'^;  the  length  of  well  to  receive  the  stairs 
13'  9'^;  tlie  rail  is  4^'  by  2K''.     Balusters  are  to  be  2'^  by  2^\ 

Fig.  1.  Shows  the  plan,  having  20  risers  and  starting  with  a 
quarter  i>ace  winding  around  a  cylinder  of  8'^  radius,  and  land- 
ing witli  a  ([uarter  pace  winding  on  a  cyHnder  of  6'^  radius  to  a 
level  (piarter  pace  at  No.  16  rise;  thence  with  four  flyers  to  the 
latuliug  in  tlie  second  story. 

The  height  of  story  from  top  to  top  of  joist  equals  12'  6^'', 
which  reduced  to  inches  equals  150'^  being  divided  by  20  risers 
(1.50''-^20=7K''),  equals  7}4^^,  as  the  heigiit  of  eacli  rise,  and 
if  we  use  a  constant  of  25'^  in  tiiis  case,  the  relative  width  of 
tread  to  rise  will  be  IC,  or  7)4'^  by  IC  for  the  pitch.  See  rule 
for  width  of  step  in  proportion  to  height  of  rise,  page  87. 

The  cylinders  are  laid  otf  so  as  to  have  the  well  hole  in  the 
center  of  well;  tlien  Nos.  2  and  16  rise  will  be  about  the  same 
U'ugth  as  at  the  flyers  or  straight  steps,  ?/  7" . 

The  walking  line  is  drawn  \h"  from  the  face  and  parallel 
with  the  outer  string.  No.  9  tread  is  placed  at  the  center  of  well 
in  this  case,  and  the  balance  of  treads  is  spaced  ofl:  on  the  walk- 
ing line  either  way  equal  to  a  regular  tread  (IC^).  Nos.  1  and  2 
treads  are  slightly  curved  and  increased  in  width  on  the  walking 
line.  The  length  of  Nos.  2  and  16  treads  should  never  be  less 
than  those  at  Nos.  9  or  20,  but  if  anything,  they  should  be  longer 
?/'  or  A^" .  If  shorter  the  stair-case Avill  have  a  contracted  appear- 
ance. An  incli  or  two  at  those  points  makes  a  great  difference 
either  way.  Draw  Nos.  7  to  11  and  also  No.  17  rise  at  right 
angles  to  the  outer  string;  then  locale  the  short  balusters  on  Nos. 
11  and  17  treads,  and  space  off  for  the  intermediate  balusters  on 
the  center  line  of  rail.  The  face  of  risers  may  now  be  drawn  to 
suit  the  balusters,  and  through  the  points  on  the  walking  line  to 
intersect  the  wall  string. 

It  will  be  observed  at  Fig.  4,  that  the  baluster  on  No.  12  step 
is  located  near  the  center  of  tread;  this  is  done  to  allow  the  bal- 
usters to  appear  near  the  same  from  centers;  the  tread  is  gradu- 
ated to  aid  the  easing  on  tiie  lower  edge  of  string..  The  face  of 
wall  string  projects  IK^''  from  the  line  of  studs,  allowing  %''  for 
lath  and  plastering,  and  \"  for  the  thickness  of  base;  No.  11 
winding  tread  is  12''''  wide  at  the  face  of  wall  string  No.  12 
ami  vi  treads  are  19);^''  and  26M'''  each.  No.  14  is  C  to  the 
face  of  string  in  the  corr.or,  and  243^''''  from  the  corner  to  face  of 
No.  1.5  rise.  No.  15  wimiing  tread  is  243^j'''  wide;  No.  7  rise  is 
^"  from  the  spring  of  circular  wall  string,  and  No.  2  rise  is  6'^ 
from  tlu>  spring  at  the  starting.  Nos.  1,  2,  3,  4  and  5  treads  arc 
each  ISM^''  wide,  and  No.  6  is  1&}4^^  wide  at  the  wall  string. 
This  quarter  pace  winding  for  a  working  drawing  should  be 
drawn  full  size  on  heavy  paper.     AA  shows  the  bearers  S'^X^'^ 


Plate  38.  IW 

seautliug,  to  which  rough  brackets  are  nailed  for  supports;  they 
are  placed  iu  position  so  as  to  transmit  the  weight  from  the  outer 
string  to  tlie  walls.  SB  shows  the  bridging  on  the  quarter  pace 
opposite  the  bearers,  the  same  should  be  done  at  the  landing. 

Fig.  2.    SJiftn's  the  clevntion. 

The  height  AB,  [12^  6^']  being  divided  into  20  risers  at  7>^'^ 
each,  the  joist  is  shov,  n  10'^  wide  and  f^  stripping  for  lathing, 
making  11^'  as  the  depth  to  allow  for  joist. 

The  height  from  floor  to  top  of  platform  is  10''  0'^.  and 
the  joist,  plastering  and  flooring  of  platform,  equals  12^^  and 
the  carriage,  lath  and  plastering,  plumb  under  and  including  No. 
15  rise,  will  equal  16^'  mere,  (12^^+16^^=-:^  4'^)  equals  2^  4''^ 
Now  tii(!  door  under  the  platform  is  7'  0^^  phis  2^  4^^  [7^  0'^+ 
2^  4^^=9'  4^^J  e(iuals  9'  4^',  this  deducted  from  the  height  of 
platform  [10'  0"—^'  i'^=0^  S^^]  equals  8^'  for  the  finish  over 
the  door  plumb  undcT  No.  15  rise. 

Often  a  full  finish  over  the  doors  and  windows  under  the 
platforms  ca-niot  bo  had.  In  this  the  stair-builder  has  to  arrange 
as  bL'st  he  can.  but  whenever  practicable,  let  the  finish  be  com- 
plete, as  that  improves  the  work. 

Headway.  Count  down  from  the  landing  14  risers  at  73^'' 
each  (U  >J>^''=Yf'''=S'  9'0,  equals  8'  9'^  from  the  top  of 
lloor  to  a]i(l  including  No.  7  rise.  The  width  of  joist,  stripping; 
flooring,  lath  and  plastering  eciuals  13'^  Then  S'  9^''  minus  1'  1^' 
equals  7'  8'^  as  the  height  from  No.  6  tread,  plumb  over  No.  7  rise 
to  the  line  of  plastering.  We  will  locate  tlie  face  of  trimmer 
plumb  over  the  center  of  No.  6  tread,  at  the  walking  liiie.  This 
will  allow  ample  head  room.  This  locates  the  trimmer  in  the 
second  floor  9'  3'''  from  the  wall  for  the  length  of  well. 

For  the  quarter  pace  at  the  lauding  iu  the  second  story,  the 
face  of  joist  is  located  6'''  from  the  face  of  No.  20  rise,  and  7'  2^' 
from  the  wall;  the  half  width  of  hall  is  i^  \'^,  and  the  radius  of 
cylinder  equals  6",  and  the  thickness  of  level  fascia  is  1'^.  Then 
tiie  width  to  trim  the  huidiug  [V  1^'— (6''-f  l'')=3'  6^'].  will  equal 
3'  6^'  by  •?/  V\  as  shown  on  plau  Fig.  1.  SS  shows  the  spring 
of  cylinder. 

The  lengths  to  measure  for  jointing  the  rail  are  shown  taken 
from  spring  to  spring  of  cyli)ider  (6'  9'^)  for  No.  1  length;  No.  2 
length  is  taken  from  spring  of  cylinder  to  face  of  No.  20  rise  (3' 
l}i'')\  No.  3  length  is  taken  from  the  face  of  landing  rise  to  tlio 
spring  of  quarter  cylhider  (2'  0^'),  and  No.  4  length  is  taken 
fnmi  spring  of  quarter  cylinder  to  wall  on  plan  (4^1'');  all  in- 
clining lengths  must  be  taken  parallel  to  the  true  pitch,  and  all 
level  lengths  parallel  to  the  floors. 

Fig  3.  Shows  the  plan  of  cylinder  at  the  newel  draivn  to 
a  H^^  iicalc. 

The  balusters  are  shown  spaced  off  on  the  center  line  of  rail, 
and  the  risers  are  drawn  iu  to  suit;  the  radius  OA  equals  8'^  for 
the  line  of  cylinder.  The  face  of  No.  6  rise  is  2%''''  from  the 
spring  of  cylinder.  The  cut-out  of  No.  6  tread  is  5Ja'';  No.  2 
step  should  be  increased  in  width,  so  as  to  give  the  proper  .space 
between  Nos.  2  and  3  balusters  and  at  the  newel  post. 

Fig.  4.  Shoivs  the  halutstcrs  spaced  off  around  the  12'^ 
crjlLnder,  and  face  of  risers  drawn  to  suit  the  spacing  of 
halustci's. 

The  nosing  line  of  steps  intersects  with  the  return  nosings 
and  gives  the  miters  for  the  return  nosings.  The  miter  on  No.  14 
step  is  very  acute,  and  may  be  relieved  by  rounding  off  at  the 


178  Plate  39. 

poiut,  as  shown  in  Fig.  5,  Plate  34.  The  face  of  No.  13  rise  is 
Z}4J'  from  the  spring  of  cylinder.  The  width  of  Nos.  11  and  12 
tread  on  the  face  string  is  8>2^''  and  5^^  each. 

Fig.  5.  Shows  how  to  obtain  the  curve  of  grounds  around 
the  head  of  a  nitch. 

The  solid  line  AB  sliows  the  line  of  plaster,  and  the  dotted 
line  CD  shows  the  line  of  studs,  the  radius  being  4^  2^^;  iJJ'shovvs 
the  diameter  of  nitch.  'With  Hnud  J  for  centers,  draw  focus  at 
Q  from  Q;  through  H  and  J  draw  the  radial  lines  indehnite; 
parallel  with  HJ  draw  a  line  tangent  to  the  semi-circle  at  K,  in- 
tersecting the  radial  lines  at  L  and  M;  tlien  LM  is  the  stretchout 
of  the  semi-circle  HKJ;  now  divide  the  diameter  HJ  into  any 
number  of  spaces,  as  1,  2,  3,  4,  &c.;  then  draw  1  X,  2  X,  3  X, 
&c.,  perpendicular  to  HJ,  and  intersecting  the  semi-ch-cle  HKJ 
at  5,  5,  &c.  From  Q  and  through  5,  5,  &c..  draw  lines  to  intersect 
the  stretchout  LM  at  (5,  6,  &c.  From  L  6.  0,  and  iWdraw  lines 
perpendicular  to  LM  indeiinite.  Draw  PR  indefinite  and  par- 
allel to  LM,  cutting  the  perpendicular  at  7,  7,  7,  &c.,  to  indi- 
cate the  edge  of  nitch. 

Now  transfer  4  X,  3  X,  Ac,  to  corresponding  points  7  4,  7  3, 
&c.,  as  shown,  and  throngli  the  points  P,  1,  2,  3,  4,  &c.,  trace  the 
curve  for  the  head  of  nicch.  Then  licrf  between  P  and  R,  and 
bend  to  the  required  circle. 


PLATE  39. 


Plato  39.  [Scale  %^'=l  foot].  Shows  the  front  and  ivall 
siriwj  for  the  stair-case,  Fvjs.  1  ami  2,  Plate  38. 

Fig.  1.  Shoivs  part  of  the  outer  strinrj  and  the  panel 
loork  underneath,  conncctlwj  the  cylinder  at  the  starthifi. 

AB  is  the  spring  of  cylinder,  CD,  EF  ninl  GH  bhow  the 
length  of  staves  in  the  rough,  and  are  taken  from  the  cylinder. 
Fig.  3,  Plate  38,  in  the  same  manner  as  explained  for  Figs..O  and  0, 
Plate  34.  Tiie  cut-out  for  No.  0  rise  is  3''^  from  the  spring  of 
cylinder,  and  the  cut-out  for  No  0  tread  is  5  34'^'.  The  width  of 
outer  string  below  the  internal  angle  of  tread  and  rise  is  7^\  The 
lower  edge  of  string  is  eased  olf  in  this  case  down  to  the  lloor, 
and  the  i>anel  work  is  made  to  suit.* 

The  first  length  [6'  9^']  for  rail  is  taken  parallel  v.ith  th(! 
internal  angle  of  the  regular  treads  from  joint  to  joint  of  cylin- 
ders.    No.  1  rise  is  shown  reduced  to  OJ^^^,  to  allow  for  the  step. 

Fig.  2.  Shows  the  \^]^]^cr  end  of  outer  string,  Fig.  1,  con- 
necting the  12''^  cylinder  at  AB,  and  also  the  lower  end  of  face 
strings  Fig.  3,  connecting  the  cylinder  at  CD.  Tiie  regular 
^t^aight  treads  7,  8,  9  and  10,  are  si)accd  off  wiih  the  dividers,  and 
the  pilchboard  is  applied  to  the  gauge  line  NP. 

.  No.  11  tread  is  8K^^  and  No.  12  is  5^^  on  the  face  string. 
The  joint  of  cylinder  is  3'a^''  from  the  cut-mit  of  No.  13  rise: 
LM,  KJ,  HG  and  EF  show  the  lenutli  of  staves  in  i\w  rougli; 
the  angles  R  and  S  are  eased  otf  to  please  the  eye;  tlic  length  iV 
W  for  the  straight  part  of  rail  is  shown  taken  from  the  spring  of 
cylinder  AB.  The  two  cylinders  may  be  tongned  and  glued  to 
this  string  at  the  bench,  and  set  up  in  the  building. 


Plati:  p,<X  179 

Pig.  3.  Shoics  the  upper  end  of  front  f^tr'nuj  Jnnilin(j  in 
the  ftceond  story. 

The  string  is  iiotclipcl  }4^^,  llio  riiifcrence  between  the  tliick- 
ncss  of  step  and  llooring.  Tlie  joist  is  10^^  deep,  and  are  lurred 
down  one  inch  with  l^^X'^  strips,  nailed  at  right  angles  to  tlio 
direction  of  joist  to  prevent  cracks  iu  the  plastering.  The  lalh 
and  plastering  is  ]4^^-  Then  the  width  of  level  fascia  (lo^^ 
-f  1^^— Js^^^llX^O  will  equal  llJs'^  as  shown;  the  face  of 
joist  is  set  back  C/^  from  the  face  of  iN'o.  '20  rise  to  allow  the 
bearers  S,  room  to  catch  well  up  on  the  joist;  the  angle  at  A, 
is  eased  oil  with  the  easement  pattern.  The  dotted  line  CD, 
sliows  a  saw  kerf,  the  end  of  string  being  halved  out  to  receivn 
the  level  fascia,  thus  forming  a  butt  joint;  some  prefer  to  make  a 
splice  joint  at  this  point. 

Fig.  4.  Shows  the  7r(tU  string  for  the  circular  part,  the 
risers  and  tread.<t  are  lined  ojf,  hut  no  housing  is  done  until 
taken  from  the  form. 

Make  a  convex  pattern  to  snit  the  curve  for  the  face  of  cir- 
cular wall  string,  Fig.  1,  Plate  .38;  make  No.  1  tread  18%'''' wide 
as  shown  on  plan;  Xo.  2  tread  is  C  to  the  spring  line  AB;  thfii 
transfer  the  balance  of  No.  2  winder  (12^^)  with  the  convex  pat- 
tern; next  develop  the  stretfhout  of  No.  3,  4,  5  and  part  of  No.  6 
tread  to  the  spring  line  CD,  in  the  same  way.  No.  7  rise  is  8''' 
from  the  spring  line  as  shown.  In  this  case  as  the  treads  at  tha 
lower  end  are  alike,  a  pitehboard  73-2 ^'XISM^''  may  be  used. 
With  the  above  pattern,  the  stretchout  of  each  step  may  be 
developed  on  the  wall  string  correct  enough  for  practice. 

No.  7  tread  is  regular  and  eqnals  10".  The  joint  EF  is 
made  in  the  center  of  No.  8  tread.  The  height  for  base  at  tht,- 
lower  end  is  8^^;  the  angles  at  J  and  H  are  eased  off  to  idease  tin; 
eye.  The  i)lank  for  this  string  should  be  dressed  np  to  an  even 
thickness  tln-oughout.  The  riser  lines  on  the  face  of  string  should 
be  very  light;  they  should  be  pencil  lines  at  first;  then  after  llu^ 
string  is  taken  from  the  drum  they  may  be  traced  with  the  knife. 
This  is  done  to  avoid  weakening  the  surface  of  string  before 
bending. 

The  string  may  now  be  grooved  on  the  back  for  keys.  Space 
tliem  off  to  the  rule  given  in  letter  press  for  Fig.  6,  DaW.  28, 
making  them  parallel  to  the  spring  lines  AB  and  CD,  or  perpen- 
dicular to  the  treads. 

Fig.  5.    Shnivs  the  tipper  end  of  Fig.  4. 

The  joint  FS  is  made  iu  the  center  of  No.  8  tread.  The 
treads  and  risers  are  laid  off  in  the  same  manner  as  described  for 
Plates  :i.5  and  36.  The  dimension  of  each  winder  may  be  t-iken 
from  the  plan  Fig.  1.  Plate  38,  on  a  slip  of  paper  for  convenience 
when  lining  off  the  string.  In  the  corner  IK''^  is  added  on  to  re- 
ceive the  short  string,  Fig.  6;  AB  shows  a  groove  in  the  corner. 

Fig.  6.  Shou's  the  wall  strinr)  connecting  Fig.  5,  and  land- 
ing on  the  quarter  pace.  .; 

At  the  lower  end  AB  shows  a  tongue  to  enter  the  groove 
in  the  corner,  shown  at  Fig.  5.  By  raising  up  6  V'''  in  the  angle 
a  snitab'e  easing  is  found  on  the  lower  end  of  Fig.  6,  and  also  on 
the  upper  end  of  Fig.  .5.  This  will  increase  the  v.idih  of  string 
at  the  external  angles  of  Nos.  13  and  14  rise,  but  this  caimot  be 
avoided  at  all  times.  The  straight  part  of  wall  string  is  lined  off 
from  the  pitch-board. 


180  Plate  40. 


PLATE  40. 

Plate  40.  [Scale  %''^=\  foot.]  Shoivs  hoxv  to  construct 
the  facc-mouhls  for  the  stair-case.  Fig.  1,  Plate  38;  the  jyJan  of 
cyllnilcr  sUirllng  being  greater  than  a  quarter  circle  and  less 
tliaii  a  semi-circle. 

Fig.  1.  Shores  the  plan  of  tangents,  enclosing  the  center 
line  of  rail  for  the  wreath-piece,  staHing  from  the  ncioel;  the 
angle  of  tangents  on  jiZaii  is  acute,  and  the  u-rcaih  to  he  worhcd 
out  in  one  piece. 

The  center  line  of  rail  AJBCU  struck  from  the  ceuter  O.  with 
a  radius  AO.  equal  to  8%^^.  The  doited  line  indicates  the  face  oi 
cylinder;  X  is  the  center  of  newel,  and  D  is  the  point  of  miter; 
C  is  the  termination  of  the  curve  at  the  cap. 

From  C  draw  CO;  perpendicular  to  CO  draw  CE  indefinite; 
perpendicular  to  AO  draw  the  tangent  to  intersect  CE  at  E; 
prolong  the  tangent  .EA  to /S  for  direction  of  straight  rail.  Fnma 
0,  and  parallel  to  CE,  draw  OK;  the  face  of  Xo.  6  rise  is  2}i^^ 
from  the  spring  of  cylinder  on  the  center  line  of  rail,  and  No,  G 
tread  measures  5M^^  as  shown.  No.  7  tread  is  a  regular  tread 
10'^  wide. 

ITig.  2.  Shows  the  elevation  of  risers,  treads  and  the 
Ungth  of  tangents. 

Let  XX  indicate  the  edge  of  drawing  board;  make  A  J"  and 
JB  equal  Air  and  KE,  Fig.  1;  perpendicular  to  XX,  draw  AC, 
Jilfand  BD  indefinite;  on  the  line  AC,  set  up  the  height  of  five 
risers,  then  elevate  Nos.  6,  7  and  S  risers,  keeping  the  face  of  N'o. 
6  rise  2}i''  from  the  spring  line  AC;  No.  G  tread  is  Ty;i'^,  and 
No.  7  tread  is  10^''.  Through  the  center  of  balusteis  0,  O,  draw  tlie 
under  side  of  rail;  parallel  with  00,  draw  the  center  of  rail, 
intersecting  AC  at  C:  from  the  lop  of  No.  1  step  set  up  i}i^'  to 
the  under  side  of  rail,  and  Ih'^'  more  to  the  center  of  rail, 
making  .5%''''  from  top  of  No.  1  tread  to  center  of  rail  at  L; 
make  i^J* equal  CD  on  plan,  Fiar.  1,  [IH''). 

From  L,  and  parallel  to  XX,  draw  LG.  Now  let  it  be 
observed  at  Fig.  1,  Plate  38,  that  the  diameter  is  prolonged  to 
intersect  the  walking  line  at  H,  on  No.  6  tread,  that  the  ladial 
line  enters  No.  5  tread  and  across  No.  6  rise,  and  in  on  No.  6 
tread,  indicating  that  the  tangents  should  be  lifted  above  No.  5 
tread  on  the  spring  line  AC,  over  one  rise,  we  will  say  to  K, 
8}i^^  in  this  case,  as  that  will  allow  at  the  same  time  a  suitable 
easing  to  connect  the  wreath-piece  witl)  the  straight  rail. 

Draw  Z/if  prolonged  to  intersect  the  center  of  rail  at  N,  and 
cutting  the  perpendicular  from  J  at  M;  from  M.  and  parallel  to 
XX,  draw  MB.  Make  GB,  equal  the  diagonal  BE,  Fig.  1; 
make  GQ  equal  the  chord  AC,  Fig.  1;  make  KS  equal  3K^^  for 
shank;  make  joint  at  S  at  right  angles  to  NK.  Draw  the  point 
Hon  the  center  of  rail  opposite  the  face  of  No.  7  rise  for  a  point 
on  the  pattern  to  measure  from,  when  jointing  the  rail;  the  dis- 
tance iJC.  is  lO^'',  which  should  be  marked  on  the  pattern:  from 
P,  draw  BT,  at  right  angles  to  LK. 

Bevels.  Let  ZZ  indicate  the  edge  of  a  board;  paralhl  with 
ZZ,  draw  9  10;  perpendicular  to  ZZ,  draw  9  H.  equal  to  the 
radius  OA,  Fig.   1,    (8%^0-     '^^^^e  9    12  equal  BT,  and  9  ^?, 


Pr.ATi.;  40.  181 

equal  GP;  draw  11  12  and  11  13  prolonged  to  edge  of  board;  the 
angle  at  1?,  gives  the  bevel  at  the  miter  cap,  and  the  angle  at  13 
gives  the  bevel  for  the  shank. 

Parallel  with  9  10,  draw  the  half  width  of  rail  (3'^),  cutting 
the  hypothenuse  of  bevels  at  14  and  15. 

Fig.  3.     Shoivs  the  construction  of  fnce-mouUl. 

Make  SKML  equal  SKML,  Fig.  2;  with  K  as  a  center,  and 
KQ  in  elevation,  Fig.  2,  for  a  radius,  draw  arc  at  C;  then  with 
L  as  a  center,  and  tlie  director  EC,  Fig.  1,  for  a  radius,  draw  arc 
intersecting  at  C;  join  LC  prolonged  to  equal  CD  {1}{^^)  on 
plan,  Fig.  1. 

Perpendicular  to  LC,  draw  CO  indefinite;  parallel  with  LC, 
draw  M0\  draw  OK  prolonged,  and  we  have  the  trapezium 
OKLC,  on  the  cutting  plane,  that  when  in  position,  will  agree 
with  the  trapezium  OAEC,  on  plan,  Fig.  1. 

Proof.  The  diagonal  OL^  must  equal  the  distance  HP, 
Fig.  3.     if  so,  the  angle  of  tangents  at  L  must  be  correct. 

Make  joint  at  /S  at  right  angles  to  SL;  make  OA  equal  the 
radius  OA,  Fig.  1,  (8%^^);  make  A  4  and  A  5  each  equal 
the  half  width  of  rail  (2^^:  make  C2  and  C  3  each  equal  13  15, 
Fig.  2;  also  make  iS  7  and  S  8  each  equal  12  14,  Fig.  2;  draw  8  G 
and  7  9  p.irallel  to  SL,  to  intersect  the  radial  line  OK  produced. 
Now  OCis  the  semi-major  axis,  and  OA  the  semi-minor  axis. 

Pivot  the  trammel  at  O  with  the  arms  resting  on  the  major  axis 
line;  for  the  concave  side  of  mould,  set  from  th"^  pencil  to  minor 
pin  the  distance  OA,  then  place  the  pencil  in  the  point  at  3,  and 
drop  the  pins  into  the  grooves,  then  fasten  the  major  pin  at  O,  and 
trace  the  curve  for  the  convex  side  of  mould;  proceed  in  like 
mar.ner  to  trace  the  center  and  concave  curves;  from  D  draw  the 
straight  wood  required  for  miter  parallel  to  OC. 

yections  P  and  i?  show  the  application  of  bevels.  Observe 
they  cross  the  tangents  in  their  application. 

Pig.  4.  Shows  how  to  obtain  the  face-mould  for  the  same 
plan  bj'  the  use  of  ordinales,  drawn  from  the  chord  line  as  a  base, 
which  is  more  convenient  than  using  a  trannnel  in  long  face- 
moulds.  The  correctness  of  curve  depends  on  the  number  of 
ordinates;  the  greater  number  of  ordinates  the  more  correct  will 
be  the  face  mould.  The  lettering  is  the  same  as  Fig.  1;  AS  and 
EC  are  tangents  to  the  center  line  of  rail  at  the  points  A  and  C. 
Draw  the  chord  AC;  bisect  the  same  at  M;  bisect  AM  and  MC 
at  iVand  P;  bisect  again  at  Quad  R;  froui  these  bisections  draw 
ordinates  parallel  with  the  director  CE,  cutting  the  concave  and 
convex  sides  of  rail  at  1,  1,  1,  and  2,  2,  2,  &c. 

Fig.  5.     Shows  the  face-mould  similar  to  Fig.  3. 

Draw  SKVL  equal  to  SKML,  Fig.  3.  With  KQ,  Fig.  2, 
as  a  radius  and  K  for  a  center,  draw  aic  at  C;  with  GL,  Fig.  2. 
as  a  radius  and  L  for  a  center,  draw  arc  intersecting  at  C;  draw 
LC  produced.  Draw  thechord  KC;  bisect  iiCCat  M;  bisectilfZir 
and  jf Cat  N  and  P;  bisect  again  at  i?  and  Q;  draw  ordinates 
from  the  points  K,  M,  N,  P,  R,  Q,  parallel  to  the  director  CL. 
Now  transfer  the  points  on  ordinates  on  Plan  Fig.  4  to  correspond- 
ing ordinates  on  face-mould,  using  the  chords  as  base  lines. 

Make  joint  at  iS  perpendicular  to  SL;  make  CD  equal  CD 
on  plan;  make  joint  at  D  perpendicular  to  Z)Z»/  make  C  3  and  C 
4  each  equal  15  13,  Fig.  2;  make  /S  8  and  S  7  each  equal  14  13, 
Fig.  3.     Draw  the  direction  of  straight  wood  at  7,  8  and  3,  4. 


183  rr.ATK  40. 

parallel  with  tho  tangents  KL  and  LC.  Then  trace  the  concave 
and  convex  sides  of  face-mould  through  the  points  3,  1,  1,  1,  8, 
and  4,  2,  2,  2,  7,  using  a  flexiijle  strip. 

If  tlie  points  of  contact  are  recjuired,  draw  CO  indefinite  and 
perpendicular  to  DZ/;  parallel  with  CL  draw  VO:  from  the  in- 
tersection at  O  draw  OK  prolonged.  Then  the  radial  lines  OC 
and  OK  give  llie  points  of  contact  connecting  the  straights  witli 
1  he  curved  part.  The  sections  at  A  and  B  show  the  bevels  np- 
plied,  same  as  at  Fig.  .". 

Proof.  The  diagonal  OL  must  equal  the  distance  PR,  Fig. 
2;  if  so,  the  triangle  KLC  la  correct. 

If  it  be  required  to  find  the  length  of  odd  balusters  at  the 
newel,  tlien  return  to  plan  Fig.  1.  Parallel  with  the  director 
CE,  draw  lines  from  the  intersection  of  each  rise  with  the  center 
of  rail  to  intersect  the  tangent  AE  at  F,  Cr,  H  and  J.  Now 
from  the  points  F,  G,  H  and  J  on  plan  draw  lines  perpendicu- 
lar to  XX  in  elevation,  Fig.  2,  showing  the  treads  and  risers  1,  2, 
3,  4  and  .'>,  in  elevation. 

Then  if  lines  be  drawn  from  the  center  of  each  baluster  in 
the  same  manner  to  intersect  the  under  side  of  rail  as  shown  for 
No.  ?>  baluster  on  No.  4  step,  which  intersects  the  tangent  at  L, 
and  again  intersects  No.  4  step  at  Y,  and  the  underside  of  rail 
at  U;  then  No.  3  baluster  is  equal  to  UY,  longer  than  a  regular 
short  baluster.  The  other  balusters  may  be  elevated  in  the  same 
way. 

Fig.  6.  Shows  plan  of  the  center  line  of  rtdl  for  the  12" 
eiilinder,  Fig.  4,  Plate  38. 

The  radius  OA  for  the  center  line  of  rail  equals  fi%'".,  AB, 
BC,  CD  and  JDE  show  the  tangents  enclosing  the  semi  circle 
ACE;  draw  the  direction  of  the  straight  string  AF  and  ECr. 
Now  show  the  direction  of  the  risers  cutting  the  tangents.  The 
face  of  No.  18  rise  is  3%^''  from  the  spring  of  cylinder  measured 
on  the  face  of  outer  string,  if  measured  on  the  center  line  of  rail, 
it  equals  "/\  When  proceeding  to  draw  the  elevation  of  treads 
and  risers,  take  the  width  of  treads  from  the  center  line  of  rail  on 
the  straight  part,  and  in  the  cylinder  follow  the  line  of  tangents. 

Fig.  7.  SIioivs  the  clcvatmi  of  tmvjents;  they  hc\n<j  un- 
folded. 

Let  ZZ  indicate  the  edge  of  drawing  board  ;  fi)id  the  average 
pitch  from  the  face  of  No.  10  rise  to  the  face  of  No.  18  rise.  Thus 

equals  04^^  measured  around  the  tangents.  Now  this  includes 
8  risers  and  8  treads.  Divide  04'''  by  8,  the  number  of  risers, 
e(|ua!s  S'^  for  the  average  tread,  the  regular  rise  is  7K'^  Ihen 
with  8^'  on  the  bhwle  of  square,  and  l!}^^^  on  the  tongue,  the 
tongue  will  give  the  average  pitch. 

Now  set  a  bevel  to  that  pitch,  and  draw  the  perpendiculars 
AF.  BG,  CH,  DJ  and  EK,  each  to  equal  AB,  BC  CD  and 
DE,  on  plan.  Fig.  G. 

Next  elevate  the  treads  and  risers,  keeping  the  face  of  No.  13 
rise  3'^  from  the  spring  line  AF,  and  No.  17  rise  comes  on  tlie 
spring  line  EK;  Nos.  12  and  11  treads  equal  .5}^^'  and  S}i" 
each;  and  No.  10  and  17  treads  eiiual  10'^  each. 

Through  the  center  of  balusters  O,  O,  and  O,  0,  draw  the  in- 
clination for  the  underside  of  rail.  Parallel  with  00  and  00 
draw  the  center  of  rail  intersecting  AF  at  L  on  the  right,  and 
on  the  left  extend  to  intersect  BG  atM,  cutting  CH,  DJ  and 


Plate  40.  183 

EK  at  HJ  and  K  respectively,  ilf  is  a  fixed  point;  from  M 
draw  MF  to  tangent  arc  at  No.  13  rise,  and  intersecting  the  cen- 
ter of  rail  at  P,  and  cntting  AF  at  Q.  From  Q  and  at  riglit 
angles  to  AF,  draw  QR,  cutting  BG  at  S.  Tliiontrh  H,  and 
perpendicular  to  AF,  draw  FHE,  cutting  BG  and  I?J"al  G  and 
N;  then  J2i2"  will  be  the  height  for  the  lower  wreath- jiiLco,  and 
i7it  willbe  the  height  lor  the  upper  wreath-piece.  I'roN.ng  tan- 
gent QM  to  intersect  HF  at  T;  also  prolong  tangent  HM  {o  in- 
tersect FQ  at  V;  from  /S  and  perpendicular  to  MV  draw  SW; 
from  G  and  at  ri^;lt  angles  to  7"^  draw  GY;  fr(.m  iV  and  per- 
pendicular to  JH  draw  NU;  make  Q  2  and  JE7;^  each  eiinal  to 
the  chord  AC,  on  plan  Fig.  6;  parallel  with  BG  draw  Ihelialf 
width  of  rail  (2^0.  cutting  HM  and  MQ  at  4  and  .0;  at  K,  ij''  is 
allowed  for  straight  wood,  and  at  Q  4'^  is  allowed. 

Ease  off  the  angle  at  P  to  form  the  ramp  agreeable  to  the 
eye. 

Bevels.  Let  XX  indicate  the  edge  of  board;  draw  Mie 
dotted  line  6  20  parallel  to  XX;  draw  6  7  perpendicular  to  XX. 
and  equal  to  the  radius  OC,  Fig.  0  (^yfi^').  Make  0  8  equal  GY, 
and  6  9  equal  UN,  and  6  20  equal  SW;  draw  7  8  and  7  U  and  7 
20  to  the  edge  of  board  for  convenience  when  setting  the  bevel. 

If  it  be  required  to  find  the  length  of  odd  balusters  in  tlie 
cylindei',  tlien  return  to  plan,  Fig.  G;  make  JSiT  equal  GT,  Fig. 
7;  connect  KC  for  the  director,  or  level  line  on  plan.  Now 
from  the  center  of  each  baluster  draw  lines  parallel  to  CK,  to 
intersect  the  tangents  AB  and  BC  for  the  lower  quadrant 
OABC;  for  the  upper  quadrant  OCDE,  the  diagonal  OD,  be- 
comes the  director  in  this  case,  because  both  tangents  in  elevation 
are  the  same  length.  Then  from  the  center  of  each  baluster 
in  the  upper  quadrant,  draw  lines  parallel  to  OD,  to  intersect  the 
tangents  CD  and  DE.  Now  transfer  the  points  on  tangents  on 
plan  to  their  position  on  the  treads,  relative  to  the  tangents  as 
shown  in  elevation,  Fig.  7.  Observe  the  baluster  on  No.  14 
tread  is  one  [l^^J  inch  longer  than  a  regular  short  l)aluster;  also 
the  long  baluster  on  No.  12  tread  is  'd}i''  longer  than  a  regular 
short  one. 

Fig.  8.     Shows  the  face-mould  for  the  lower  wrcath-piecc. 

Make  AB  equal  QM,  Fig.  7;  with  A  as  a  center,  and  2  F, 
Fig.  7,  for  a  radius,  draw  arc  at  C;  again  with  B  as  a  center,  and 
tangent  jEfM,  for  a  radius,  draw  arc  interseeting  at  C;  join  BC; 
parallel  with  BC  and  BA,  draw  AO  and  CO,  for  the  parallelo- 
gram OCBA,  on  the  cutting  jilane. 

Proof.  The  diagonal  OB  must  equal  V  2,  Fig.  7;  make 
AD  e(iual  TM.  Fig.  7.  Draw  OD  for  the  director;  make  OF 
equal  OC,  on  plan.  Fig.  6;  make  F  2  and  i^oeacli  equal  the 
half  width  of  rail;  make  A  4  and  A  .5  eaeii  e<iual  M  4.  Fig.  7, 
and  C  (■),  C  7  each  equal  M  5,  Fig.  7.  I'ivot  the  traniniel  at 
O  with  the  arms  at  right  angles  lo  OF,  and  set  from  the 
pencil  to  nunor  pin  the  distance  OF  for  the  center  of  rail; 
then  j)iace  the  pencil  in  C,  and  drop  the  pins  iido  the 
grooves,  and  trace  the  center  line  on  the  faee-niould  For  the 
concave  side,  set  from  pencil  to  minor  pin  the  distance  O  2,  then 
lilace  the  pencil  in  the  point  at  (5,  and  drop  the  pins  into  the 
grooves,  then  fasten  the  major  pin  and  trace  the  curve  G,  2,  4; 
repeat  the  operation  fov  the  convex  side. 

Make  joint  at  H  4^-'  from  A,  and  at  right  angles  to  BA, 
draw  4  8  and  5  9  parallel  to  BH;  make  joint  at  C  perpendicular 
to  BC. 


184  'Plate  40. 

The  ^ecfcioJis  Q  and  /S  show  the  ai^plicalion  of  bevels.  The 
bevel  sho  "i  a.,  30,  Fig,  7,  applies  at  Q,  and  the  bevel  shown  at 
8,  Fig  '(  aopaes  at  the  section  marked  S.  Note  the  bevels  cross 
the  tangents. 

Fig.  9.  Shoivs  the  facc-mouhl  for  the  ripper  wreath-piece, 
the  tangents  hcing  hath  the  one  leng-h,  hence,  the  diagonal  on 
the  cuUing  plane  will  he  the  director,  or  direction  of  the  minor 
axis,  and  only  one  bevel  rvill  be  required  for  both  Joints. 

Make  ED  equal  tangent  KJ,  Fig.  7;  let  EL  equal  C/^  for 
shank,  as  shown  at  K,  Fig.  T;  with  ^  as  a  center,  and  3  K,  Fig. 
7,  for  a  radius,  draw  arc  at  C;  then  wiih  JDE  as  a  radius,  and  D 
for  a  center,  draw  arc  intersectinir  at  C;  join  DC;  parallel  to  DE 
and  DC,  draw  the  radial  lines  CO  and  EO  for  the  parallelogram 
OEDC,  on  the  cutting  plane. 

Proof.  The  diagonal  OD  must  equal  the  diagonal  OD,  on 
plan,  Fig.  6. 

Make  OA  equal  the  radius  OC,  Fig.  6;  let  A  2  and  A  3  each 
equal  the  half  width  of  rail  (^''0;  niake  C 4,  C 5  and  E  6,  El, 
each  equal  M  4.  Fig.  7;  make  joints  at  L  and  C  perpendicular 
to  the  tangents  DL  and  DC;  draw  6  S  and  7  9  parallel  with  EL. 

Pivot  the  trammel  at  O,  with  the  ;irras  at  right  angles  to  the 
director  OD;  set  from  pencil  to  minor  pin  the  distance  OA,  then 
place  the  pencil  at  C,  and  enter  the  minor  pin  in  the  groove; 
at  the  same  time  slide  the  major  pin  until  both  pins  enter  the 
grooves,  then  fasten  the  major  pin  and  sweeii  the  curv<;  through 
the  points  CAE;  the  curve  must  tangent  DE  and  DCatthe 
]>oints  Cand  .£7  always,  if  not,  the  work  must  be  gone  over  again 
and  corrected.  If  the  elliptic  curve  should  cross  the  tangents  at 
the  points  C  and  E.  or  should  it  fall  short,  the  learner  will  he 
sure  the  mould  is  not  correct. 

The  sections  S  and  J"  show  the  bevels  applied  through  the 
center  of  mould.  The  bevel  shown  at  9.  Fig.  7,  is  applierl  at  both 
joints.  The  distance  LE  shows  the  amount  of  straight  wood 
(6'''  to  allow'  when  cutting  the  straight  rail. 

Fig.  10.  Shows  the  easement  pattern  landing  in  the  second 
story.  The  under  side  of  inclining  rail  is  made  to  pass  through 
the  center  of  balusters  O,  O,  on  No.  19  and  20  tread,  and  the 
under  side  of  level  rail  is  lifted  above  the  floor  half  a  rise  (o^'i'^); 
the  face  of  No.  ;20  rise  is  show-n  on  pattern  at  2.  The  amount  of 
straight  wood  is  3^^  as  shown  for  the  inclining  part,  and  for  the 
level  from  the  face  of  No.  20  rise  to  the  joint  on  easement,  equals 
V  o"  to  allow  when  cutting  and  jointing  the  rail.  For  con- 
venience, these  measurements  .should  be  marked  on  the  pattern. 

Jointing  the  rail.  The  easement  pattern  over  Nos. 
G  and  7  treads.  Fig.  2,  shows  \\}"  from  the  spring  of  cylinder 
to  the  fixed  point  H,  marked  on  the  pattern.  And  tlie  ramp 
pattern  over  Nos.  11  and  12  treads,  Fig.  7,  shows  \'  ^"  from  the 
spring  of  cylinder  to  the  fixed  point  I,  also  mark  on  the  pattern. 
These  points  shoidd  be  transferred  to  the  crook,  so  as  to  be  seen 
on  the  under  side  of  rail,  when  bolted  together  for  proving  the 
exact  lengths  before  leaving  the  shop. 

Tlie  length  from  spring  to  spring  of  cylinder  equals  6^  ^"  for 
A^o.  1  length,  (see  Fig.  2.  Plate  38);  now  deduct  the  two  meusure- 
nienls  almve  (lO'^+l^  9^^=:2^  7^^)  from  the  whole  Icngtli  (i')^  9'^— 
9/  V^\f  2")  equals  4'  1"  between  the  two  fixed  points  H,  Fig. 
2,  and  I,  Fig.  7. 


Platk  41.  185 

For  No.  2  Icngtii.  TIic  shank  at  Fig.  9,  is  6''''  long,  and  the 
easement  pattern  at  Fig.  10,  shows  3'^  from  the  joint  to  the  fixed 
point  2,  and  the  whole  length  from  spring  of  cylinder  to  face  of 
landing  rise,  equals  3^  IK^';  from  which  deduct  the  above  (3'' 
IK'^— (C^'+3^0=2MX^0  equals  2^  4K^^  the  length  to  cut 
No.  3. 

For  No.  3  length.  We  have  1'  ?>"  to  the  joint  on  easement 
pattern  to  be  deducted  from  the  whole  length  '7/  Q"  fiom  face  of 
No.  20  rise  to  spring  of  quarter  cylinder,  which  (2^  0^''— 1^  3''''= 
0^  9'^)  equals  9^^  for  the  short  length,  the  shank  of  quarter  turn 
may  be  increased,  aad  one  joint  made  to  answer;  from  quarter 
turn  to  wall  is  4''  V. 


PLATE  41. 


Plate  41.  [Scale  M'^=l  foot].  Exhibits  two  different 
face-moulds  for  a  quarter  j:)ac.ervinding,  starting  froni  a  newel,  and 
having  five  winders;  the  regular  tread  is  10''''X~''^  rise. 

Fig.  1.  Shows  a  quarter  circle  starting  from  a  6''''X6'''' 
neivel,  with  five  winders. 

The  radius  OA  for  the  face  of  outer  string  equals  \2'\  the 
distance  AB  is  15'''  from  the  face  of  string  for  the  walking  line. 
The  regular  tread  10^'',  is  spaced  off  on  the  walking  line;  No.  1 
tread  is  swelled  and  increased  to  11 1-^^''  on  the  regular  tread  line; 
the  balusters  should  be  spaced  off  equal,  and  the  risers  drawn 
from  tiie  l)alusters  through  the  spacing  on  the  walking  line;  in 
this  case  it  will  be  ol)served  that  No.  3,  4  and  5  risers  radiate  to 
the  center  O,  and  No.  2  rise  nearly  so;  now  if  the  radius  OA  be 
prolonged  to  cut  the  walking  line  at  B,  it  will  be  seen  in  this 
case  that  the  line  BO  remains  on  No.  G  step  from  the  intersection 
at  the  spring  of  cylinder  to  the  intersection  of  the  walking  line, 
hence  a  person  walking  up  or  down  the  stairs,  the  hand  will  be 
normal  to  the  curve  of  rail.  Wherever  the  stair  builder  can 
arrange  his  winders  in  this  way,  more  satisfaction  will  be  the 
result. 

The  center  of  newel  is  5'^,  and  the  point  of  mitre  is  4''^  from 
the  spring  line  OC,  Fig.  2.  On  the  face  of  wall  string.  No.  1 
ticad  is  15'^;  No.  2,  18  J4'';  No.  3  is  27^'  to  corner:  No.  4,  27'^; 
No.  5,  19'^,  and  No.  6  is  the  regular  tread  IC  wide;  these 
measurements  may  be  marked  from  the  drawing  made  to  the  full 
size,  on  to  the  scale  drawing,  or  a  slip  of  paper  for  convenience, 
when  lining  off  the  wall  string. 

At  No.  3  winder,  a  temporary  pattern  made  of  thin  lath  is 
shown  tacked  and  braced;  this  pattern,  by  turning  over,  will 
answer  for  No.  4  winder;  patterns  may  be  made  for  the  other 
winders  and  all  strujig  up  until  needed,  and  the  drawing,  if  made 
on  paper,  may  be  rolled  up  for  future  use.  The  lining  out  of  the 
wail  and  front  strings  is  the  same  as  previously  described. 

Fig,  2.  Shows  the  plan  of  tangents  AB  and  BC,  inclos- 
ing tJie  center  line  of  rail  ADC. 

The  radius  OA,  of  the  quarter  circle  ADC,  equals  V2%^^; 
the  center  of  newel  is  located  C  from  tiie  quarter  circle,  and  the 
point  of  miter  is  4'^  from  the  sjiring  line  OC;  the  face  of  No.  7 
rise  is  8}^^^  from  the  spring  line  OA;  the  dotted  line  ^^indi- 
cates the  face  of  cylinder,  the  radius  of  which  is  12^''. 


186  Plate  41. 

Fig.  3.  Shoios  the  cicvelopment  nf  ianoenis  from  plan  Firj. 
2,  the  dertilion  nf  treads  and  riftcrs,  and  aho  the  tanfjcnts  for 
face-mould. 

Let  XX  iiulicato  the  edge  of  drav.'ing  board;  make  AB  and 
BC  equal  AB  and  BC,  Fig.  2,  perpeiidieular  to  XX:  draw  AD, 
i5i7aud  CF,  indefinite.  At  A,  set  up  the  licight  of  G  risers,  and 
elevate  the  treads  and  risers  from  their  intersection  with  the  tan- 
gents on  plan,  Fig.  2;  mal?e  the  face  of  No.  7  rise  8^'^  from  the 
spring  line  AD.  Tln-ougli  the  center  of  balusters  O,  O,  draw  tlie 
underside  of  rail  parallel  with  00,  ch-awtlie  center  of  rail,  cutting 
AD  at  G;  mark  tlie  point  H,  on  the  center  of  rail,  plumb  over 
No.  7  rise,  for  a  fixed  point  when  cutting  the  straight  rail. 

Now  4^^  to  the  right,  and  jiarallel  with  CF,  draw  tlie  point 
of  miter  JK;  from  the  top  of  first  step  set  up  r/^  to  the  underside 
of  rail,  and  I'^i  more,  or  QH^^  to  the  center  of  rail  at  Z.  We  are 
now  ready  to  elevate  the  tangents;  if  a  radial  line  be  drawn  to 
the  center  of  No.  2  step.  Fig.  1.  on  the  walking  line,  as  OC,  it 
will  be  seen.  The  line  is  all  on  No.  2  step,  and  indicates  that  tlie 
direction  of  steps  is  very  near  normal  to  the  curve  of  cylinder 
or  rail,  and  the  position  at  Cwill  tlierefore  admit  of  keeping  the 
rail  down  to  the  regular  height  of  a  short  baluster.  Tlien  we  will 
in  this  case  give  the  lower  tangent  the  inclination  of  No.  2  tread 
and  rise,  as  sliown  at  SS:  draw  the  underside  of  rail  parallel  with 
SS:  draw  the  tangent  imlefiuite  for  the  center  of  rail,  cutting 
CF  at  L  and  BE  at  N,  and  at  the  same  time  intersecting  a  level 
line  from  Z,  say  at  n,  so  as  to  allow  a  small  easing  into  tlie  cap. 

From  N,  draw  the  upper  tangent  to  intersect  GH,  at  any 
point  beyond  G,  sufficient  to  form  an  easing  connecting  the  wreath 
with  the  straight  rail,  we  will  say  at  M,  and  cutting  AD  at  P, 
prolong  FN  to  intersect  CF  at  Q;  parallel  with  XX  draw  LR, 
cutting  BEKi  T;  parallel  willi  XX  draw  GU.  cutting  LN.  ]>ro- 
diiced  at  V.  From  27,  and  perpendicular  to  VL,  draw  J7W; 
from  T,  and  perpendicular  to  PQ,  draw  TY;  parallel  with  BE, 
draw  the  lialf  width  of  rail,  cutting  LN  and  iVPatUandlO. 
Make  R  12  equal  the  chord  ACou  plan,  Fig.  2;  make  P  1'.)  equal 
twice  NU,  prolong  the  tangent  NL  to  intersect  JK  at  in. 

Bevels.  The  dotted  line  14  1.5,  indicates  a  gauge  line  par- 
allel with  XX;  at  right  angles  to  XX,  draw  1.5  16,  ecpial  to  tlic 
radius  OC,  Fig.  2;  make  15  17  equal  UW,  and  15  14  equal  TY, 
join  14  and  1(>,  and  17  16;  the  angles  at  14  and  17;  give  the  bev- 
els required;  make  P  IS  equal  2^^  for  shank  on  face-mould. 

Fig.  4.    Shoivs  the  face-mould. 

At  any  convenient  place  on  the  pattern  paper  draw  JBClo, 
equal  to  NL  lo.  Fig.  ;];  with  C  as  a  center  and  P  12.  Fig.  H,  for  a 
radius,  draw  arc  at  A;  again,  with  B  as  a  center,  and  tlu^  tangent 
PN,  Fig.  :;.  for  a  radius,  draw  arc  intersecting  at  A;  draw  BA 
prolonged,  parallel  with  AB  and  BC,  draw  CO,  and  AO  pro- 
duced, for  the  parallelogram  OABC,  on  the  cutting  plane,  or 
plane  of  plank. 

Proof.  The  diagonal  OB  must  equal  the  distance  12  19,  Fig. 
3;  if  so,  the  angle  of  tang(>nts  at  B  must  be  correct.  Make  CD 
equal  NV,  Fig.  3,  draw  DO,  ]>roduced,  for  the  direction  of  the 
minor  axis;  make  OF  equal  the  radius  OC,  Fig.  2;  make  F2  and 
F3  each  equal  tlie  half  width  of  rail  [2'^^  make  A  4  and  A  5 
each  e(iual  N'J,  Fig.  3  ;  make  CO  and  C7  each  equal  iVlO,  Fig. 
3;  draw  0  8  and  7  '.)  parallel  with  B  13;  make  joint  at  13,  perpen- 
dicular to  tangent  B  13,  and  the  joint  at  H,  make  at  right  angles 
to  tangent  AB ;  draw  4  10  parallel  to  HB.    Now  pivot  the  tram- 


Plate  41.  ISt 

incl  at  0,  and  set  from  pencil  to  minor  pin  the  distance  OF,  for 
the  center  of  rail  on  the  face-mould;  then  place  the  pencil  in  tlie 
point  at  A,  and  drop  the  pins  in  the  si'ooves;  then  fasten  the 
major  pin  and  trace  the  cnrve  for  the  center  of  rail  on  th(^  face- 
mould  shown  by  the  dotted  line  AFC;  now  draw  the  concave 
and  convex  sides  of  mould  in  the  same  way. 

The  bevel  shown  in  the  angle  at  IT,  Fig.  3,  is  applied  at  sec- 
tion L,  and  the  bevel  shown  in  the  angle  at  14,  Fig.  3,  is  shown 
applied  at  section  N. 

For  the  joint  at  L,  connecting  the  newel  cap,  make  the  joint 
and  apply  the  bevel  in  the  usual  way.  After  the  bevels  have 
been  applied,  and  the  wreath  piece  dressed  off  to  the  plumb  on 
the  concave  and  convex  sides,  then  draw  the  line  2  2  through  the 
center  of  crook  as  shown  at  section  L,  and  apply  the  bevel  .shown 
in  the  angle  at  13,  Fig.  3,  from  the  joint  and  through  the  points 
2,  2  giving  the  plumb  cut  JK,  Fig.  3,  from  which  lay  off  the 
center  of  rail  Zn,  Fig.  3,  the  distance  to  13  Z  above  the  point  13. 
A  short  piece  may  be  glued  on  the  upper  side  of  crook  to  increase 
the  tliickness  of  plank  for  the  easing,  if  required,  as  shown  at  00. 

The  section  at  L  shows  the  block  pattern  lifted  up  from  13  to 
Z,  at  the  center.  Now  shape  the  easing  at  right  angles  to  the 
joint  JK,  as  shown. 

To  obtain  the  length  of  odd  balasters,  make  CH  on  plan, 
Fig.  2,  equal  VU  in  elevation.  Fig.  3;  join  OH  for  the  director 
on  plan.  From  the  center  of  Nos.  3,  4  and  5  baluster,  draw  lines 
to  intersect  CB  and  BA  at  9,  B,  and  10;  now  transfer  the  point 
marked  10  on  No.  5  tread,  also  the  poiut  9  on  No.  3  tread,  and 
the  intersection  at  B  on  No.  4  tread  on  plan,  Fig.  2  to  corre- 
sponding treads  in  elevation.  Fig.  3,  as  shown. 

The  bxiluster  on  No.  4  tread  happens  to  come  on  the  angle 
line  BE;  now  elevate  the  balusters  parallel  to  the  perpendicular, 
to  intersect  the  underside  of  rail  as  shown. 

As  the  short  baluster  at  O  is  naught,  then  the  baluster  on  No. 

3  step  will  be  equal  to  }4^^  longer,  and  on  No.  4  step  \H'^,  and 
on  No.  5  step  Ifi^^  longer  than  a  regular  short  baluster. 

Fig.  8.  Shoivs  hoiu  the  easing  at  the  upper  end  of  ivrrath- 
plcce  may  be  irnrkcd  on  the  shanli  of  same,  and  tlius  avoid  the 
short  cashaj  HM,  Fig.  3.  , 

PA  shows  tise  tangent  NG,  Fig.  3,  prolonged;  also  GB  for 
the  inclination  GH,  Fig.  3.  Through  5,  draw  the  joint  3  4  per- 
pendicular to  the  straight  rail  BG;  setoff  on  each  side  of  PA, 
the  half  thickness  of  plank  required  for  the  wreath-piece,  shown 
at  seclion  N,  Fig.  4;  make  a  temporary  joint  at  A,  at  right  angles 
to  AP,  as  2  3;  to  this  joint  apply  the.  bevel  in  the  nsual  waj% 
shown  at  N,  Fig.  4,  and  work  off  the  wrtath-piece  to  the  plumb 
on  tlie  concave  and  convex  sides;  then  apply  the  bevel  .shown  at 
2,  from  the  temporary  joint,  for  the  cripple  joint  3  4.  Now  drop 
the  block  p.ittern  on  the  joint  just  made  the  distance  A  5,  below 
the  center  of  jtlank  for  tin;  center  of  rail  as  shown;  then  ease  off 
into  the  wreath  part,  from  a  tangent  at  right  angles  to  the  joint 

4  3,  thus  saving  tlie  short  straight  easing. 

Fig.  5.  Shov-s  another  treatment  of  the  plan,  Fig.  2;  the 
radius  [12%''']  for  center  of  rail,  the  position  of  treads  and  ris- 
ers being  the  same. 

AB,  BC,  are  the  tangents;  the  face  of  No.  7  rise  is  SK'"' 
from  the  spring  of  cylinder. 


188  Plate  41. 

Fig.  6.  Shows  the  elevation  of  treads  and  risers,  al&o  the 
tancjents. 

The  upper  tangent  is  allowed  to  have  the  same  inclination  in 
this  case  as  the  straight  rail;  hence  the  wreath-piece  will  contain 
its  own  natural  easing  all  in  the  wreath  part  of  rail,  at  the  upper 
end.  In  this  case  a  joint  is  made  at  the  spring  line  at  the  lower 
end,  and  a  small  easing  is  added  to  connect  the  newel  cap,  as 
shown. 

Let  XX  indicate  the  edge  of  drawing  board,  make  AB  and 
SCeach  equal  AS,  BC,  on  plan,  Fig,  5.  Perpendicular  to  XX 
draw  AD,  BE  and  CF  indefinite.  Now  elevate  the  treads  and 
risers  from  the  tangents  on  plan.  Fig.  5,  making  No.  7  rise  ^}4'' 
from  the  spring  line  AD.  Through  the  center  of  balusters  O,  O, 
draw  tiie  underside  of  rail.  Parallel  with  00,  draw  the  center  of 
rail,  cutting  AD  at  P,  and  BE  at  N,  and  prolonged  to  intersect 
CF  at  Q;  from  the  top  of  No,  1  step  set  up  5^^  to  the  underside 
of  rail,  and  lU^''  more,  or  6)^^''  to  the  center  of  rail  at  Z;  draw 
Zn  parallel  to  XX. 

From  the  center  of  baluster  on  No,  2  tread,  draw  the  arc  for 
center  ot  inclining  rail.  From  N,  draw  a  line  to  tangent  the  arc 
and  intersect  the  horizontal  line  from  Z  at  n,  and  also  cutting  CJP 
at  L;  make  joint  at  L  perpendicular  to  DN,  and  draw  easing  to 
suit.  From  P  draw  PU  parallel  with  XX,  cutting  LN  pro- 
duced at  V.  From  L  draw  LR  parallel  with  XX,  cutting  BE 
at  T;  from  T  and  at  right  angles  to  PQ,  draw  Tjr;  from  U, 
and  at  right  angles  to  LY,  draw  WU;  parallel  with  BE,  draw 
the  half  width  of  rail  (:y^)  cutting  the  tangent  PiV  at  10,  an.d  the 
tangent  NL  at  9;  make  R  12  equal  the  chord  AC,  on  plan,  Fig. 
5;  at  P  allow  G'-'  for  straight  wood  on  the  shank  of  face-mould; 
make  P  19  equal  LQ. 

Bevels.  Let  14  15  indicate  a  gauge  line  parallel  with  XX; 
perpendicular  to  XX,  draw  15  16  equal  to  the  radius  OC,  Fig.  5. 
Make  15  18  ecpial  Ty,  Fig.  0,  and  15  17  equal  WU,  Fig- 6;  draw 
16  18  and  16  17  prolonged  to  edge  of  board. 

Fig.  7.  Shoivs  the  fucc-moidd  lined  ojf  from  the  chord 
line,  by  the  7(se  of  ordinates  transferred  from  the  plan  direct. 

Make  BC  equal  NL,  Fig.  6;  with  C  as  a  center,  and  P  12, 
Fig.  6,  for  a  radius,'  draw  arc  at  A;  again  with  S  as  a  center, 
and  PN  for  a  radius,  draw  arc  intersecting  at  A:  join  BA  and 
prolonged  to  H,  allowing  6'^  for  shank.  Parallel  with  AB  and 
BC,  draw  CO  and  AO,  for  the  parallelogram  OABC,  on  the 
cutting  plane. 

Proof.  The  diagonal  OB  must  equal  the  distance  12  19  Fig. 
6,  if  so,  the  angle  of  tangents  at  B  must  be  correct. 

Make  joints  at  H'and  C  perpendicular  to  the  tangents  AB 
and  BC;  make  CD  equal  NV  Fig.  C;  join  OD  and  produced  for 
the  points  in  face-mould,  through  which  to  trace  the  concave  and 
convex  curve  using  a  pliable  strip. 

Draw  the  inside  and  outside  curve  of  rail  on  plan,  Fig.  5; 
make  Cff  equal  UV  Fig.  6,  connect  OH  for  the  director;  bisect 
the  clioni  AC  at  D;  bisect  AD  and  DC  at  E  and  F;  now  parallel 
with  OH,  and  from  the  points  A,  E,  D,  Pand  C,  draw  ordinates 
to  cut  the  concave  and  convex  curves  of  rail  ou  plan,  as  E.  2, 
3,  4.  &c. 

Now  return  to  Fig.  7,  bisect  the  chord  AC  at  D;  biscci  DA 
and  DC  at  E  and  F;  parallel  to  the  director  OD,  draw  ordinates 
indefinite  from  the  points  A,  E,  D,  F  and  C,  then  transfer  the 
points  on  the  ordinates  ou  plan,  Fig.  5,  to  corresponding  ordinates 


Plate  42.  189 

ou  face-mould,  using  the  chords  for  base  lines;  make  OJ  equal 
the  radius  OC  on  plan,  Fig.  5;  make  J" 4  and  J^  each  equal  the 
half  ^^idtl^of  rail  (;y^);  make  C2  and  C3  each  equal  iVlO,  Fis:.  6, 
also  make  A  G  and  A  7  eat-li  CMjual  iV9,  Fig.  6;  parallel  with  IrlB, 
draw  6  8  and  7  9  for  the  width  of  face-mould  at  the  shank.  The 
curves  may  now  be  drawn  through  the  points  just  found,  using  a 
pliable  strip. 

At  sections  P  and  J2  the  bevels  are  shown  applied  to  cross 
the  tangents. 

Bahisters.  If  required  to  find  the  length  of  odd  baluster  in 
the  quarter  circle  on  the  center  line  of  rail,  then  from  the  center 
of  each  baluster  ou  phm.  Fig.  5,  draw  lines  parallel  witli  the 
directing  ordinate  OH,  to  intersect  the  taugeuts  as  at  XXX, 
Fig.  5. 

Now  transfer  their  intersection  with  the  treads  ou  tangents 
on  plan,  to  corresponding  treads  in  elevation.  It  will  be  noticed 
that  the  balusters  ou  No.  4  winder  does  cross  No.  4  rise  and  ou  to  No. 
3  wiuder  on  plan,  and  is  set  over  on  line  wilh  No.  4  tread  in  eleva- 
tion. Fig.  6,  as  the  proper  place  for  its  length.  Now  parallel 
with  tli(^  risers,  draw  the  balusters  to  intersect  the  underside  of 
rail  at  //,  »fec.,  for  their  respective  lengths,  as  explained  for  Fig.  3. 

It  will  be  observed  that  after  tlic  d  i  reel  or  Oi^fou  plan,  is  located, 
the  position  of  risers  under  llie  tanirtuts  in  elevation,  relative 
to  the  cutting  plane  may  bo  establLslicd;  for  each  ordinate  on 
face-mould  is  horizontal  and  parallel  to  corresponding  ordinates 
on  plan,  and  all  parallel  to  the  directing  ordinates. 

It  will  be  oI)served  at  Fig.  0,  tlie  tangent  PN,  is  in  line  with  the 
center  of  straight  rail,  thus  avoiding  the  easing  shown  at  Fig.  3. 
This  has  caused  the  rail  to  raise  at  iV-,  and  as  a  result,  the  balusters 
are  longer,  and  ihe  rail  will  feel  liigh  when  standing  on  No.  4 
step;  while  at  Fig.  3,  the  rail  will  Jiave  an  agreeable  lieight; 
but  it  is  a  good  fault  that  the  rail  on  winders  be  high  better  than  to 
feel  low. 

On  quarter  and  half  pace  winding  stairs  the  rail  should  never  be 
constructed  so  that  the  wreath-piece  would  line  with  tlie  nosings, 
unless  the  risers  ail  radiate  to  the  center,  and  at  the  same  time, 
be  for  a  large  cylinder,  or  in  a  circular  stair-case,  then  the 
wreath  may  be  constructed  so  that  when  placed  on  the  stairs, 
the  underside  of  rail  will  touch  every  nosing.  When  as  in  this 
case  the  tangent  PN,  Fig.  0,  is  the  continuation  of  tlie  straight 
rail;  there  shordd  not  be  more  than  one  graduating  step  outside  the 
cylinder,  or  the  space  of  a  regular  trciid,  may  start  from  the  spring 
of  cylinder  at  the  upper  end  of  v.inders,  while  at  the  lower  end, 
they  should  be  graduated;  one  fault  to  tlus  method  is,  without  the 
use  of  graduated  steps  at  the  upper  end,  Die  easing  on  the  lower 
edge  of  front  string  will  be  difticult  to  malce  s;itisfactory,  as  the 
string  has  to  be  increased  more  than  usual  at  t  he  angle  in  the  forma- 
tiou  of  the  casing  couuecting  the  regular  treads  with  the  winders. 


PLATE  42. 


Plata  42.  Exhibits  jilan  (Fig.  1)  of  a  half  pace  divided 
into  ticu  quarter  paces  Inj  pldcmij  two  risers  across  the  half  pace. 

This  is  done  in  many  cases  to  gain  room  and  avoid  winders. 
The  well  hole  is  10''^  diameter,  and  the  pitch  is  8^^  wide  by  9^^ 
tread.  No.  14  tread  is  placed  in  the  center  of  half  pace,  and  the 
balusters  are  to  be  spaced  olf  on  the  center  line  of  rail  equally,  and 
then  the  risers  are  curved  to  t-uit  the  balusters  and  the  miters  at 
the  return  nosings. 

Also  at  Fig.  2  is  shown  a  quarter  pace  winding;  the  radius  of 
quarter  cylinder  is  13^'.  In  this  case  we  have  placed  No.  16  tread 
in  the  center,  and  spaced  the  olluns  either  way  on  the  walking 
line.  Nos.  13  and  20  are  the  fust  square  risers  outside  the  wind- 
ing treads.    Locate  a  short  baluster  ou  Nos.  13  and  30  tread; 


190  Plate  42. 

then  space  the  iuterveuing  balusters  equally,  and  draw  the  risers 
through  the  points  on  the  walking  line  to  suit  the  balusters.  The 
scale  for  Figs,  1  and  2  is  }/i''  equal  1  foot. 

Fig.  3.  [Scale  M^^^l^-]  Shotvs  ijlan  of  the  W  cylindefi; 
Fl'j.  1. 

The  dotted  line  indicates  the  string,  and  solid  line  the  center 
line  of  rail,  AB.  BC,  CD  and  JD^  show  the  tangents  enclosing 
the  center  line  of  rail.  The  balusters  are  spaced  off  around  the 
cylinder,  and  the  concave  and  convex  risers  are  curved  into  the 
cylinder  to  suit  the  balusters.  The  face  of  Nos.  12  and  17  rise 
are  2>4'''^  from  the  spring  of  cylinder,  the  radius  of  cylinder  being 
5'^  and  balusters  2^'X2^''.  Then  the  radius  for  the  center  line  of 
rail  will  equal  5%''^  or  the  diameter  for  the  center  line  of  rail 
will  equal  IIK^^ 

Fig.  4.  Shows  the  elevation  ^f  taiujents,  treads  and  risers, 
unfolded  from  the  tangents  on  'ijlan  Fig.  3, 

Let  XX  indicate  the  edge  of  drawing  board;  the  points  A, 
B,  C,  D  and  J57show  perpendiculars  draAvn  from  XX,  and  indi- 
cating the  spring  A  and  angle  B,  center  C  and  angle  D  and 
spring  E,  on  plan  Fig.  .3.  Now  elevate  the  risers  and  treads  from 
the  tangents  on  plan  Fig.  C,  being  careful  to  keep  the  face  of  No. 
12  and  17  rise  2^i'^  from  the  spring  lines  A  and  E,  as  shown  on 
plan  Fig.  3.  Throu>:h  the  center  of  balusters  O,  0  and  O,  O  draw 
the  underside  of  rail;  parallel  with  00,  on  the  right,  draw  the 
center  of  rail,  cutting  the  spring  line  at  E,  and  to  intersect  the 
angle  and  center  lines  at  B  and  F,  and  also  intersecting 
the  spring  line  on  the  left  at  G.  Now  D  becomes  a 
fixed  point.  At  the  external  angle  of  No,  12  rise  draw  arc  equal 
to  the  half  thickness  of  rail  (I  i^'^),  and  from  JD  draw  a  line  to 
tangent  the  arc  and  intersect  the  center  of  rail  at  H,  and  cutting 
the  center,  angle  and  spring  lines  at  C  B  and  A;  from 
A,  and  square  to  the  spring  line  C,  draw  AJ.  cutting  the 
angle  line  B  at  K:  then  JC  will  be  the  height  fm-  the  lower 
wreath-piece;  from  C,  and  square  to  the  spring  line  E.  draw  CL, 
cutting  the  angle  line  D  at  M;  then  LE  is  the  height  for  the 
upper  wreath-piece. 

Square  to  LE,  draw  EN,  cutting  the  angle  line  D  at  P; 
prolong  the  taiiiient  CD  to  intersect  iV^  at  Q;  from  B,  and  per- 
pendicular to  CQ,  draw  PR;  from  M,  draw  MS  stiuare  to  EF\ 
make  CT  and  JU  equal  the  chord  AC,  Fig.  3:  draw  KV  at 
right  angles  to  AB;  parallel  with  the  angle  line  D,  draw  the  lialf 
width  of  rail,  cutting  the  tangent  DE  at  2,  and  the  tangent  CD 
at  3;  ease  the  angle  on  the  left  at  H  to  please  tlie  eye;  make 
joint  on  easement  so  as  to  allow  3'''' of  straight  wood  on  the  shank 
of  face-mould. 

Bevels.  Let  4  5  indicate  a  gauge  line  parallel  with  XX; 
square  to  XX,  draw  4  6,  and  equal  to  the  radius  OC,  Fig.  3; 
make  4  7  equal  PR,  make  4  8  equal  KV,  also  make  4  5  to  equal 
MS;  draw  6  5,  6  8  and  6  7  to  the  edge  of  board. 

As  the  two  tangents  AB  and  BC  for  the  lower  wreath-piece 
are  both  the  same  length,  and  inclination,  one  bevel  only  will  be 
required  for  both  joints,  the  angle  at  8  gives  that  bevel. 

The  tangents  CD  and  DE  for  the  upper  wreath-piece  are  of 
different  inclinations  and  will  require  two  bevels;  the  angle  at  5 
gives  the  bevel  for  shank,  and  the  bevel  iu  tUe  angle  at  7  gives  the 
bevel  for  ceuter  joiut. 


Plate  42.  191 

Fig.  5.    Exhibits  the  face-mould  for  the  lower  ivreath-piccc. 

Make  AB  equal  the  tangent  AB,  Fig.  4:  with  A  as  a  center 
and  CU,  Fig.  4  for  a  radius,  draw  arc  at  C:  again  with  B  as 
a  center,  and  BA  for  a  radius,  draw  arc  intersecting  at  C,  join  BC. 
rarallel  with  BA  and  BC,  draw  CO  and  AO  for  the  parallelo- 
gram on  the  cutting  plane,  that  will  coincide  with  the  parallelo- 
gram O ABC  on  plan.  Fig.  3.  when  in  position. 

Proof.  The  diagonal  BO  must  equal  BO  on  plan.  Fig.  3. 
Draw  the  diagonal  BO  for  the  direction  of  minor  axis;  prolong 
the  radial  lines  OA  and  OC;  make  A  '2,  A  3.  also  C  4,  eacli 
equal  jD  3,  Fig.  4;  make  OD  equal  the  radius  OC,  Fig.  3;  make 
D  6.  D  7,  each  equal  the  half  width  of  rail  [2^^J;  make  from  A 
to  F  equal  3''  for  shank;  make  joint  at  F  square  to  the  tangent. 
Now  draw  the  right  angle  at  O.  and  trace  the  concave  and  convex 
sides  of  mould  by  using  the  rod  as  described  at  Fig.  9,  Plate  13. 

The  sections  at  Jif  and  J"  show  the  bevels  applied  to  cioss  the 
tangents,  and  through  the  center  of  plank.  The  shaded  part 
shows  the  width  at  the  joints  to  saw  out  the  crooks.  At  the 
crossing  of  minor  axis,  %^^  wider  than  the  mould  on  the  concave 
side,  is  all  the  over-wood  that  will  be  required  in  this  case;  that 
amount  will  allow  the  twist  of  rail;  at  this  point  the  bevels  blend, 
and  the  section  is  at  right  angles  to  the  face  of  crook. 

Fig.  6.    Exhibits  the  face-mouJa  for  tlie  upper  wreath-piece. 

Make  CD  equal  tangent  CD,  Fig.  4,  with  C,  as  a  center,  and 
NT,  Fig.  4,  for  a  radius;  draw  arc  at  E;  again,  with  D 
as  a  center  and  DE,  Fig,  4,  for  a  radius,  draw  arc  intersecting 
at  E,  draw  DE.  prolonged  6'^  to  H;  parallel  with  DE  and  DC, 
draw  CO  and  EO,  for  the  i^arallelograni  on  the  cutting  plane. 

Proof.  The  diagonal  DO  must  equal  TF  in  elevation.  Fig. 
4;  make  CA  equal  DQ,  Fig,  4.  Draw  OA  indefinite  for  the 
direction  of  minor  axis.  Make  OB  equal  the  radius  OC,  Fig.  3. 
Prolong  the  radial  lines  OC  and  OE:  make  E  2  and  E  3  each 
equal  D  3,  Fig.  4;  make  B  .5  and  B  4  each  equal  the  half  width 
of  rail  (2^0;  make  C6  and  C7  each  equal  D  2,  Fig.  4. 

Make  joints  at  Cand  iiZ"  square  to  the  tangents  CD  and  DE. 
Draw  3  9  and  2  S  parallel  with  DH.  Draw  the  right  angle  to  the 
minor  axis  at  O,  and  trace  the  concave,  convex  and  center  curves 
of  face-mould,  using  a  rod  to  make  points  in  the  curve,  then  use 
a  pliable  strip  in  tracing  the  curves,  -j 

The  section  at  P  shows  the  bevel  at  the  angle  7,  Fig.  4, 
applied  through  the  center  of  plank;  the  section  at  R  shows  the 
bevel  found  in  the  angle  at  5,  Fig,  4,  applied  through  the  center 
of  plank,  for  the  shank  end  of  wreath-piece. 

Fig.  7.  Exhibits  the  plan  for  the  quarter  pace  icinding. 
[Scale  %"=l  foot]. 

The  dotted  line  indicates  the  face  of  outer  string,  and  the 
solid  line  the  centre  line  of  rail.  The  radius  for  the  center  line  of 
rail  equals  VZ%''\  the  tangents  AS  and  SC  inclose  the  quarter 
circle  and  are  at  right  angles  to  each  other;  the  face  of  No  14 
and  19  rise  is  9Ai  from  the  spring  of  cylinder;  Nos.  13  and  19 
treads  are  634^'' on  the  center  line  of  rail;  Nos,  13  and  20  treads 
are  the  regular  width,  9''', 

Fig.  8.  Exhibits  the  development  of  tangents  AB  and  BC, 
from  the  plan.  Fig.  7,  and  also  the  treads  and  risers. 

Let  JCX  indicate  the  edge  of  drawing  board;  at  right  angles 
to  XX  draw  the  spring  and  angle  lines  A,  B,  C;  elevate  the 
treads  and  risers  from  the  tangents  on  plan,  keeping  the  face  of 


]9'2  Plate  43. 

Nos.  li  and  19  rise,  3)^'''',  from  the  spring  lines;  Nos.  13  and  19 
treads  are  6H^^  wide,  and  Nos.  13  and  30  are  9^^  wide.  Note,  at 
Fig.  3,  the  radial  lines  intersect  the  regular  tread  line  by  crossing 
No.  19  rise,  and  also  crossing  No,  14  rise,  tlius  indicating  tliat  the 
rail  should  be  kept  np  at  No.  19  rise,  while  at  No.  14  the  rail 
should  be  kept  dowu."^" 

Through  the  centre  of  balusters  0,  O  and  O.  0  drav/  the  under- 
side of  rail  parallel  with  the  underside  of  rail;  draw  the  center  of 
rail,  intersecting  the  spring  line  at  D  on  the  left  and  at  .Eon  the 
right;  now  we  will  allow  the  direction  of  upper  tangent  to  cross 
the  spring  line  at  C,  level  with  No.  19  tread,  making  a  small 
easing  to  connect  the  wreath-piece.  Take  a  point  say  at  G,  and 
draw  GC  prolonged,  cutting  the  angle  line  at  JB,  and  intersecting 
the  spring  line  at  J".  At  the  center  of  balusi-er  on  No.  14  tread 
draw  arc  e<iual  to  the  balf  thickness  of  rail;  from  B  draw  line  to 
tangent  the  arc,  cutthig  the  spring  line  at  A,  and  intersecting  the 
center  of  rail  at  H,  square  to  the  Fjninii  line;  from  A  draw  AJ, 
catting  the  angle  line  at  K\  tlien  JC  will  be  the  height  the 
wreath-piece  will  raise  from  center  to  center. 

From  C,  and  square  to  CJ,  draw  CL,  cutting  the  angle  line 
at  M;  prolong  tlie  tangent  AB,  to  inter.-^ect  CM  at  N;  from  M, 
and  square  to  BN,  draw  MP;  from  iT,  and  square  to  BF,  draw 
KQ;  make  AR  equal  the  chord  AC,  Fig.  7.  Parallel  with  the 
angle  line  at  B  draw  the  half  width  of  rail  (3^^),  cutting  the 
tangents  at  3  and  3.  Allow  3^^  at  A  and  C  for  straight  wood  on 
the  shank  of  face-mould.  Make  the  joints  square  with  the  tan- 
gents AB  and  BC;  ease  off  the  angles  at  H  and  G  to  please 
the  eye, 

A  plumb  line  over  Nos.  13  and  30  rise  at  tlie  center  of  rail, 
will  serve  as  points  to  calculate  the  length  of  straight  rail.  To 
the  points  2>  and  E  there  are  llli'^\  mark  this  on  the  pattern,  as 
shown. 

Bevels.  The  dotted  line  4  5  indicates  a  gauge  line  parallel 
witli  XX;  make  4  S  on  the  perpendicular  line  equal  the  radius 
OC  Fig.  7:  make  4  6  equal  MP;  let  4  5  equal  KQ\  draw  S  6 
and  <S  5  prolonged  to  edge  of  board. 

Fig.  9.     Shows  the  face-mould. 

Make  AB  equal  the  tangent  AB,  Fig.  8;  with  A  as  a  center, 
and  RL,  Fig.  8,  for  a  radius,  draw  arc  at  C;  rgiin  with  B  as  a 
center,  and  BC,  Fig.  8,  for  a  radius,  draw  arc  inlersectaig  at  C; 
connect  BC:  parallel  with  tangents  BA  and  BC,  draw  AO  and 
CO,  for  the  parallelogram  ABCO,  on  the  cutting  plane. 

Proof.  The  diagonal  BO  must  equal  RF,  Fig.  8;  make  AD 
equal  BN,  Fig.  8.  Draw  JDO  for  the  director,  at  right  angles  to 
the  director  at  O  draw  the  scat  for  the  trannnel;  make  OF  equal 
OCon  plan;  make  F2  and  F5  each  equal  half  width  of  rail  (3^''). 
Let  A  4,  A  5  each  equal  B  ".  Fig.  8.  and  C  6,  C  7  each  equal 
B  3,  Fig.  8;  make  AH  and  CJ  each  3'^  for  straight  wood  con- 
necting the  ramp  and  easing;  make  joints  at  H  and  J,  at  right 
angles  to  the  tangents  BA  and  BC;  draw  4  8  and  6  9  parallel 
with  the  tangents. 

*  The  inclination  to  give  llie  langontB  over  winders  in  elevation 
In  iiiiiny  eases  will  retiuiie  the  best  judfjnient  of  tlio  stair-linilder. 
This  lie  will  le;un  from  practice  — where  to  raise  or  lower  llic  tan- 
gents, KO  that  the  i  ail  will  have  an  agreeable  height,  neither  too  high 
nor  dangerously  low. 


Plate  43.  193 

Now  if  a  trammel  is  not  at  hand,  and  tliis  lieing  a  long  face- 
mould,  less  room  will  be  required  l)y  making  use  of  tlie  ordinates; 
or  the  stair-builder  can  make  use  of  Uie  rod  and  lind  points  in  the 
curve,  tlien  use  a  flexiT)le  strip  in  tracing  the  concave  and  convex 
sides  of  mould;  wlieii  the  triimmel  is  usod  to  trace  tlio  contouf  of 
face-mould,  tiie  center  line  should  also  be  traced  on  llie  mould,  for 
it  serves  as  a  guide  to  the  correctness  of  mould,  as  llio  ciivve 
must  tangent  the  tangents  at  the  points  A  and  C;  if  llie  trinumel 
should  fail  in  this,  then  either  the  trammel  or  pins  on  the  rod  arc 
misplaced. 

The  section  at  N  shows  the  bevel  at  6,  Fig.  8,  applied  through 
Ihe  center  of  plank;  the  section  at  L  shows  the  Ijevel  found  in 
the  single  at  5,  Fig.  8,  and  is  applied  from  the  face  of  plank, 
tlirough  its  center. 

If  it  be  required  to  find  the  length  of  odd  balusters,  then  pro- 
long tangent  AB  on  phin,  Fig.  7,  making  BD  equal  MN,  Fig-.  8,  join 
D(J  for  the  director  on  plan;  from  the  center  of  each  baluster,  dr;iw 
lines  parallel  with  the  director  to  intersect  the  tangents  on  plan. 

Now  transfer  these  points  on  tlie  tangents  to  tlie  corresponding 
treads  in  elevation,  and  erect  perpendiculars  to  intersect  the  under- 
side of  rail  as  shown.  The  regular  short  b:i luster  at  No.  lU  tread  is 
naught,  and  on  No.  M  tread  a  i^"  longer;  No.  15  is  %"  longer;  on 
No.  1(5  tread  the  baluster  is  2li"  lon^-cr;  No.  17  is  i'-i"  longer;  No. 
18,-1%"  longer,  and  on  No,  19  tread  a"  longer  than  a  regular  .short 
baluster.  Supposing  the  regular  sliort  baluster  to  be  2'  2"  from  top 
of  step  to  underside  of  r;iil,  tlien  the  baluster  on  No.  19  tread 
would  he  2'  2"  plus  a"  equals  2'  5"  for  its  length  from  top  of  step 
to  underside  of  rail  at  the  center  of  baluster. 


PLATE  43. 


Plate  43.  ExhU)lL-i  ]ioiv  to  olitain  the  face-moulds  iiithrcc 
pieces'^-  (irouiul  a  soni-circlc  cu}itavtiu(j  ticvcii  winders;  tlve  railis 
hIkjicu  fur  a  rUjht  luind. 

Fig.  1.  [Scale  }4'^=1  foot.]  ISJioivs  plan  of  a  'naif  pace 
icindcr. 

Tlieic  arc  two  f;;iadiiatiiig  heads  outside  ol  llic  cylinder  on 
each  side.  The  diameter  ol  cylinder  i^j  ;J0'^;  llie  rei^ular  tread 
line  is  ir>'^  Irorn  the  lace  of  cylinder;  tlie  tread  i.s  iO-'^  by  7^^  rise, 
No.  12  ri.M!  is  placed  on  tlie  center  of  half  pace,  and  the  rejrulai' 
tread  (10^^)  is  spaced  oil  from  that,  riglit  and  left  on  tlie  walking 
line.  Tiie  balusters  are  then  si)aced  olf  equally,  and  llie  risers 
drawn  thnnvuh  tiie  points  on  tlie  walkint;-  line  to  the  wall  siring  and 
tlie  outer  string  to  suit  the  spacing  of  balusters;  the  balusters  are 
■Z^^  by  2'',  and  rail  o'^by  i'\  double  moulded. 

Fig.  2.  [Scale  K'^=l  foot.]  Exhihils  the  phtn  for  the 
center  line  of  rail;  Hie  radiiifi  OA  for  the  semi-circle  ABC 
equals  lO^ii^''.     The  dotted,  line  slioics  the  face  of  outer  striiuj. 

The  face  of  Ncs.  8  and  16  rise  are  514^^  from  the  sjiring  of 
cylinder  on  the  outer  string,  the  width  of  No.  7  and  10  treads,  is 
.'■/^  and  No.  (i  and  17,  are  regular  treads  10'^  wide  on  tlie  horse; 
the  balusters  are  ',i^^X,-y^. 

*Mr.  Simon  DeGraff  claims  the  first  to  advance  the  system  of 
making  three  pieces  in  the  wreath  around  a  semi-circle. 

10 


194  Plate  41 

Divide  the  semi-circle  ABC  into  three  equal  parts  *  as  AD, 
DE  and  EC;  draw  the  joints  at  D  aiul^,  radiating  to  the  center 
O,  draw  the  tangents  AF,  FD,  DG,  GE,  EH  and  HC,  each 
perpendicular  to  the  radial  lines  OA,  OD,  OE  and  OC;  they 
must  equal  each  other  in  this  rase  to  b :^  correct. 

Parallel  with  tanL'cnts  AF  and  ED,  draw  DJ  and  AJ  for 
the  parallelogram  AFDJ,  on  plan;  tlse  semi-cirde  being  divided 
into  three  parts  at  ^and  D,  then  the  tangent  A  J' will  equal  half 
the  diagonal  OF,  and  the  diagonal  Ji^will  equal  the  length  of 
tangent  AF:  prolong  the  tangent  AF.  From  D,  and  at  right 
angles  to  AF  prolonged,  draw  DK. 

Fig.  3.  Shows  the  development  of  tangents  from  the  plan. 
Fig.  2;  the  treads  and.  riscvfs  are  elerated  from  the  tangents  on 
plan. 

Let  XX  indicate  the  edge  of  drawing  board;  now  find  the 
average  pitch  from  tangents  on  plan,  as  explained  at  Plate  ill; 
then  draw  the  perpendiculars  AB,  CI),  EF,  GH,  JK,  SM  and 
NP,  to  the  average  pitch,  from  the  edge  of  board  XX,  all 
parallel  to  each  other  and  the  same  distance  apart,  and  eijual  to 
AF,  FD,  DG,  GE,  EH  and  HC,  on  plan,  Fig.  2. 

Now  elevate  the  treads  and  risers  from  the  tangents  on  plan, 
being  careful  to  keep  Nos.  5  and  16  rise  3>^^^  from  the  spring 
lines  AB  and  NP.  Nos.  7  and  10  treads  are  each  5'^  and  Nos. 
(5  and  17  treads  are  W^  each;  the  risers  and  treads  are  sho\^  n  by 
the  dotted  Ihies,  as  taken  from  the  tangents  on  plan  Fig.  2. 
Through  the  center  of  balusters  0,0  and  O,  Otlraw  the  undertudr 
of  rail  parallel  with  the  underside  of  rail;  draw  the  center  line  of 
straight  rail,  cutting  the  spring  line  AB  at  Q  for  the  lower  end. 
and  at  the  ujiper  end  prolong  the  center  line  to  intersect  the  per- 
pendicular JKa%  R,  and  cutting  Z,iVf  at -S,  and  NP  At  N.  At 
the  center  of  baluster  on  No.  8  tread  draw  arc  eipial  to  the  half 
depth  of  rail  (3''^);  from  ^Sdiaw  a  line  to  tangent  the  arc  and  in- 
tersect the  center  of  rail  at  T,  and  al?o  cutting  the  perpendiculars 
at  A,  C,  E,  G  and  J.  Make  joints  at  E  and  J,  as  they  are 
]ioints  of  eontactf  witli  the  center  line  of  rail,  as  .shown  at  JDand 
JE7,  on  plan  Fig  'Z. 

At  right  angles  to  AB,  draw  AF,  culling  the  perpendicular  CD 
a(  D,  then  FE  will  l)e  the  height  for  the  lower  Avreath-i)iecc; 
perpendicular  to  EF d\i\\^  EK,  cutting  GH i\t  H,  then  K.T  vviil 
be  the  height  for  the  middle  wreath-piece;  at  right  angles  lo  JK 
draw  JP,  cutting  the  perpendicular  from  L  at  M,  then  PN  is 
the  height  for  the  upper  wreath-piece.  Paiallel  with  JP  diaw 
NL,  cutting  JS  prolonged  at  u:  nuike  LV,  MW .\ud  D  'I  each 
equal  i^ir  on  plan,  Fiif.  ti;  from  V,  and  perpendicular  to  tangent 
JS  produced,  draw  Y .\,  and  from  W,  and  at  right  angles  to  NR 
draw  W  4;  from  y,  and  at  right  angles  to  AC,  draw  j^O;  make 
FZ  and  P  9  each  equal  the  chord  AD  on  plan,  Fig.  2. 


"The  radius  of  any  circle  will  divide  that  circle  into  6  enunl 
parts,  or  the  sciid-circlu  into  :jc(iual  parls,  l)CC!uise  the  radius  is  tins 
chord  of  (SO  doEcreos  of  the  cir(;lc.  Whcu  dividiiis  a  circle  into  .sc;i- 
iiionts,  it  will  I)o  found  the  l)etter  uay  to  make  the  cliord  of  each 
.se"nier)tei|\i:il  the  radius  of  the  circle,  Ihen  llic  lenj^tli  of  each  tan- 
•lent  AF,  VB,  on  plan,  will  equal  the  dia;_-onal  FJ  of  tlieii' parallelo- 
2r:inis,  and  will  aLso  e(iual  one-half  thediay;onal  OF. of  the  trapezium 
i)AVD,  both  on  plan  and  face-mould,  as  shown  at  Figs.  4  and  5,  and 
also  at  Figs.  5,  6  and  7,  Plate  44. 

+At  these  points  of  contact  the  direction  of  the  tangents  cannot 
be  cban<;ed.  The  points  C,  O  and  S  are  the  angles,  and  answer  to  the 
atislcs  F,  G,  Jf,  on  plan  Fiii.  2.  At  these  points  the  directioji  of  tan- 
■rents  may  be  changed.  The  student  in  stair-building  will  do  well  to 
remeuibc'r  this. 


Plate  43.  195 

Bevels.  Let  5  5  indicate  the  edge  of  a  board,  and  the 
dotted  line  indicates  a  gauge  line;  perpendicular  to  5  5  draw  20  21 
equal  to  KD  on  plan,  Fig.  2:  make  20  22  equal  V3,  and  20  23 
equal  jr2.  and  20  24  equal  W  4;  draw  21  22,  21  23  and  21  24 
prolonged  to  the  edge  of  board  5  5  for  the  bevels  required; 
parallel  with  5  5  draw  the  half  width  of  rail,  cutting  the  hypoth- 
enuse  of  triangles  at  a,  b  and  d. 

Fig.  4.  Shoios  the  face-mould  for  the  lower  wreiith-{yiece 
connecting  the  ramp. 

Make  AB  equal  .AC in  elevation.  Fig.  3;  with  A  as  a  center, 
and  EZ,  Fig.  3  for  a  radius,  draw  arc  at  C;  again  with  JB  as  a 
center,  and  BA  for  a  radius,  draw  arc  intersecting  at  C  join 
BC;  parallel  with  BA  and  BC  draw  CD  and  AD  for  the 
parallelogramASCZ)  on  the  cutting  plane. 

Proof.  The  diagonal  BD  must  equal  the  diagonal  FJ  on 
plan.  Fig.  2.  if  so,  the  parallelogram  is  correct. 

Make  BO  equal  FO,  on  plan,  P'ig.  2,  and  OF  equal 
the  radius  AO  on  plan.  Fig.  2.  Make  AH  equal  3"  for 
the  shank  connecting  the  ramp;  make  joints  at  If  and  C 
perpendicular  to  tangents  AB  and  BC.  Draw  the  radial 
lines  AO  and  CO  for  the  points  of  tangencji  make  F  2 
and  F  3  each  equal  the  half  width  of  rail  {IH/^);  make 
H 4,  Ho.  also  C6,  C  7.  each  equal  5  b,  Fig.  3;  parallel  with 
HB  draw  4  8  and  5  9.  Now  pivot  the  trammel  at  O,  and  trace 
the  concave  and  convex  sides  of  face-mould.  If  preferred,  bisect 
the  chord  AC,  and  draw  the  ordinates  as  has  been  explained.  By 
making  a  joint  at  A.  shown  by  the  dotted  line,  this  face-mould  will 
answer  for  the  middle  wreath-piece,  because  the  length  of  tan- 
gents and  heights  is  equal  in  both  cases. 

The  sections  at  L  and  N  show  the  application  of  the  bevel. 
Only  one  bevel  is  required  for  both  joints,  and  is  shown  at  the 
angle  23,  Fig.  3.  The  same  bevel  applies  for  the  middle  wreath- 
piece.     Observe  the  bevels  cross  the  tangents. 

Fig.  5.    Shoirs  the  faee-mould  for  the  uiqicr  irrcath-picre. 

In  this  case,  the  tangents  being  unequal,  two  bevels  will  be 
re(iuired,  and  also  observe  from  the  elevation.  Fig.  3.  they  will 
not  cross  the  tangents,  as  the  long  tangent  JS  produced  cuts  the 
horizontal  line  LN  between  the  perpendicular  LM  Aud  the  point 
V.     The  learner  will  tind  this  explained  at  Fig.  9,  Piate  14. 

Make  AB  eijual  to  JS,  Fig.  3.  With  A  as  a  center  and  9  N, 
Fig.  3,  tor  a  radius,  draw  arc  at  C;  then  with  B  as  a  center,  and 
tangent  SN,  Fig.  3  for  a  radius,  draw  arc  intersecting  at  C:  draw 
reproduced  to  F,  equal  to  (>"  for  the  length  of  straislit  wood 
on  shank.  Parallel  with  AB  and  JBCdraw  CO  and  AO  for  the 
parallelogram  on  the  cuttintr  plane. 

Proof.  The  diagonal  BO  must  equal  the  distance  MR.  Fig. 
3.  Prolong  tangent  AB,  to  D,  equal  to  Su,  Fig.  3;  join  DC  lor 
the  director;  the  curve  of  face  mould  may  now  be  drawn  by 
ordinates  or  with  the  trammel,  if  with  the  trammel,  prolong  the 
diagonal  BO  e()ual  to  itself,  to  H,  through  H,  and  parallel  to 
the  director  DC,  draw  HJ" equal  to  the  radius  OA,  Fig.  2.  10>'4  ", 
then  JH  is  the  semi-minor  axis;  draw  the  radial  line  HC  pro- 
longed, which  gives  the  point  of  tangency  on  mould;  make  joints 
at  A  and  F  perpendicular  to  tangents  BA  and  BF;  make  F2 
and  F3  each  equjil  5  d.  Fig.  3;  draw  2  4  and  3  b  parallel  with 
the  tangent  BC;  make  A  6,  A  7  each  equal  5  a.  Fig.  3;  make 
J  8  and  J" 9  'iach  equal  the  half  width  of  rail  (IK^O  •  Now  pivot 
the  trammel  at  H,  with  the  arms  perpendicular  to  JH,  and  set 


196  Plate  43. 

from  pencil  to  minor  pin  the  distance  HJ  for  the  center  lino  on 
face-mould,  then  place  the  pencil  in  C  and  the  minor  pin  in 
the  groove,  at  the  same  time  sliding  the  major  pin  on  the  stem 
until  ))oth  pins  drop  into  the  grooves,  then  fasten  the  major  pin 
and  trace  the  center  line;  proceed  in  liiie  manner  to  trace  the  con- 
cave and  convex  sides  of  mould. 

Ramp.  Mark  tlie  face  of  Xo.  7  rise  on  the  rarnp  ah  T;  then 
TQ  sliows  the  amount  (10^^)  to  allow  when  jointing  the  rail;  at 
the  upper  end  the  sliank  of  face-mould  shows  6^'  to  be  deducted. 

The  sections  at  M  and  iVshow  the  application  of  the  bevels. 
The  bevel  shown  at  22,  Fig.  3,  is  applied  at  M.  and  the  bevel 
shown  at  24,  Fig.  3,  is  applied  at  N.  Observe  they  do  not  cross 
the  tangents.  The  shaded  part  shows  the  required  widtli  to  saw 
out  the  crook  from  the  plank,  also  the  thickness  of  i)lank  required 
to  contain  the  twist  of  wreath-piece. 

If  ordinates  be  preferred  for  tracing  the  cni-ve  of  face-mould 
instead  of  a  trammel,  then  prolong  tangent  EH,  on  i)lan  Fig.  2. 
to  Z»,  equal  to  Z»Z7,  Fig.  3.  Join  LC  for  the  director  on  plan;  DC 
is  the  director  on  mould  Fig.  .5.  Now  bisect  the  chords,  draw 
ordinates  and  transfer  points  from  plan  to  face-mould,  as  described 
in  former  plates. 

Fig.  6.  [Scale  k'^^^l  foot,].  Exhibits  the  ])l(m  of  a 
quarter  pace  windlmj  at  the  laiidlmj. 

The  cylinder  being  struck  from  two  different  radii,  12''^  and 
6'\  as  shown  for  the  cjdinder  line;  tlie  tread  line  on  the  winders 
is  \?/'  from  the  face  of  cylindcM-;  tlie  balusters  are  2^''  by  S^', 
and  the  rail  is  Z^^  by  4'",  double  moulded;  the  rise  is  Q'',  and  the 
regular  tread  10'^ 

Fig.  7.  Shows  the  plan  of  the  center  line  of  rail  ACS. 
struck  from  Die  centers  M  and  N,  their  radius  hciiaj  VZ%'^  and 
0%'^,  respectively.     [Scale  %^^=1  foot.] 

Draw  the  tanirents  AB,  BC.  CD  and  DE  at  riglit  angles  to 
the  radial  lines.  Tlie  tangents  for  the  upper  wreath-piece  loiui 
an  acute  angle  at  D.  arid  the  two  lower  tangents  form  an  obtuse 
angle  on  plan  at  B-,  parallel  with  AB  and  .BC  draw  CO  and 
AO;  draw  the  chord  CE.  and  the  diaguiuil  BO  produced  to  M. 

Bisect  CE  at  F:  draw  the  diagonal  FD.  The  face  of  Xo. 
14  rise  is  l]^/'  from  tlie  spring  line  of  cylinder;  No.  1^  tread  is 
S>.^^;  No.  12,  the  regular  tn-ad,  W^.  From  C  draw  CH  per- 
pendicular to  AB  i)rolonged;  again  from  C  draw  CJ  perpenilic- 
ular  to  tangent  DE. 

Fig.  8.  Slioics  the  tniKjcnts  unfolded  from  plan,  and  the 
cleviUion  of  the  treads  and  risers  from  the  tawjents  on  plan; 
also  the  increased  leiKjth  of  the  tangents  in  elevation,  for  the 
facc-moulil. 

Let  XX  indicate  the  edge  of  drawint;  I)o;uil.  then  with  the 
bevel  set  to  tlie  average  piteli.  draw  A3,  CD.  EF.  GH  and  JK, 
to  correspond  to  tangents  AB,  BC,  CD  and  DE.  on  ])lan,  Fig, 
7.  Now  elevate  the  treads  and  risers,  keeping  tJie  face  of  No. 
14  rise  l^i'^  from  the  spring  line  AB,  as  shown  on  plan.  No.  13 
tread  is  S}-^^'  wide,  and  No.  12  tread  is  the  regular  width  HV^. 
Tlirough  tli*^  center  of  balusters  O,  0,  tlruw  the  underside 
of  rail.  I'arallel  witli  llie  underside  of  rail,  draw  the  center 
of  rail,  to  cut  the  spring  line  AB  at  L.  Mark  the  fac-, 
of  No.  13  rise  on  tlie  center  line  of  rail'  at  M,  then  ML 
equals  12M''''  to  allow  when  jointing  the  straight  rail  to  the 
ramp.     At  the  lauding  set  up  half  a  ri&e  (4^'')   to  the  under- 


Plate  43.  19% 

side  of  rail,  plus  the  half  thickness  of  rail  {2^^),  equals 
C/^  to  the  center  of  rail  from  the  floor  line.  Then  draw  FN 
parallel  to  the  floor  line.  Now  J*  is  a  fixed  point.  At  the 
external  angle  of  No.  14  rise,  draw  arc  equal  to  the  half  thick- 
ness of  rail,  and  from  the  fixed  point  JP,  draw  the  inclination  of 
tangents,  to  tangent  the  arc  and  intersect  the  center  of  inclining 
rail.  This  happens  to  be  at  Q.  The  inclination  of  tangents  cuts 
the  perpendiculars  at  A,  C,  ^andP,  and  the  level  tangent  at 
P  and  N.  From  A,  and  perpendicular  to  AB,  draw  AF,  cutting 
the  angle  line  C  at  D.  Then  FE  is  the  height  for  the  lower 
wreath-piece.  From  E,  and  perpendicular  to  EF,  draw  EH, 
then  HP  is  the  height  for  the  upper  wreath-piece.  Make  HR 
equal  the  chord  EC,  on  plan.  F\s.  7.  Let  HS  equal  the  diagonal 
DF,  on  plan,  Fig.  7.  Make  DU  equal  BH,  on  plan,  and  PV 
equal  DJ,  on  plan,  Fig.  7.  From  V,  and  perpendicular  to  tan- 
gent EP  prolonged,  draw  VW,  and  from  U,  and  perpendicular 
to  tangent  AC,  draw  Ujr.  Bisect  PH  at  Z.  Make  FT  equal 
the  chord  AC,  ou  plan,  Fig.  7. 

Bevels.  Let  ?>  3  indicate  the  edge  of  board,  and  4  4a  gauge 
line,  make  4  5  equal  HC  on  plan,  Fig.  7,  and  4  6  equal  JC  on 
plan,  Fig.  7.  Make  4  7  equal  Uy,  Fig.  8,  and  4  8  equal  VW, 
Fig.  8,  and  4  9  equal  the  height  HP,  Fig.  8;  draw  6  4,68  and 
5  7  prolonged  to  8  3.  Then  the  angle  at  7  gives  the  bevel  for  both 
joints  on  the  lower  wreath-piece,  as  both  tangents  have  the  same 
inclination.  The  angle  at  8  gives  the  bevel  for  the  lower  joint  on 
the  upper  wreath-p'ece,  and  the  angle  at  4  gives  the  bevel  for  the 
upper  joint. 

Parallel  with  4  4  draw  the  half  width  of  rail,  cutting  the 
hypotheuuse  of  triangles  at  a,  b  and  d. 

Fig.  9.    Shows  the  face-mould  for  the  lower  tvrenth-jriece. 

Make  tangent  A3  equal  AC,  Fig.  8:  with  A  as  a  center,  and 
TE,  Fig.  8  for  a  radius,  draw  arc  at  C;  again  with  B  as  a  center, 
and  BA  for  a  radius,  draw  arc  intersecting  at  C,  join  BC;  par- 
allel with  AB  and  BC,  draw  CO  and  AO  for  the  parallelogram 
ABCO  on  cutting  plane. 

rroiif.  The  diagonal  BO  must  equal  the  diagonal  BO  on 
plan,  Fig.  7.  Prolong  BO  to  e(iual  JBilf  on  plan.  Fig.  7;  through 
A  and  Cdraw  the  radial  lines  MC  a.ni\  MA  to  give  the  points  of 
tangency;  prolong  BA  .y  to  D  for  straight  sliaidt,  as  shown  at 
ramp  in  elevation.  Fig.  8;  make  joints  at  D  and  C  square  to  the 
tangents;  make  2)2  and  D'S,  also  C4  and  C5  each  equal  7  a. 
Fig.  8;  make  MF  equal  the  radius  MC,  Fig.  7.  Let  FG  and 
J* 7  each  equal  the  half  width  of  rail  \IM^^\-  parallel  with  DB 
draw  a  S  and  3  9.  Nov/  pivot  the  trammel  at  M,  with  the  arms 
at  right  angles  to  MF,  then  set  from  pencil  to  minor  pin  the  dis- 
tance MF,  place  the  pencil  in  the  point  A  and  drop  the  pins  into 
the  grooves,  and  trace  the  center  line  of  rail  through  the  points 
AFC;  repeat  the  operation  for  the  concave  and  convex  side  of 
face-niould.  At  sections  P  and  N,  one  bevel  is  shown  applied  to 
both  joints  taken  from  the  angle  at  7,  Fig.  8. 

Pig.  10.  Shoivs  the  face-mould  for  the  landing  wrcath- 
irlcce. 

^  Make  tangent  AB  equal  EP,  Fig.  8.  With  A  as  a  center, 
and  RP,  Fig.  8,  for  a  railius,  draw  arc  at  C;  again  with  B  as  a 
center,  and  PN  for  a  radius,  draw  arc  intersecting  at  C;  draw 
BC  prolonged  to  D,  'i,"  for  straight  wood  connecting  the  level 
rail.     Draw  the  chord  line  CA  perpendicular  to  tangent   CB; 


i98  Plate  44. 

draw  C£7 indefinite.  Bisect  tlie  eliord  AC  at  F;  draw  tlie  diag- 
onal BF  prolonged,  ir.teisecting  CE  at  H;  draw  HJ parallel  with 
JSC,  and  equal  to  EN,  {G%^^),  Fig,  7. 

Proof.  The  diagonal  BF  must  equal  the  distance  SZ, 
Fig.  8. 

Make  J  2  and  J  3  each  equal  the  half  width  of  rail  (IK''''). 
Make  joints  at  D  and  A  square  to  the  tangents  AB  and  BC; 
make  0*4  and  C  5  equal  9  d,  Fig.  8,  and  A  6,  A  7,  each  equal  to 
8  b.  Fig.  8.  Now  pivot  the  trammel  in  H  with  the  arms  resting 
in  the  major  axis  CH;  then  for  the  center  line  of  rail,  set  from 
pencil  to  minor  pin  the  distance  HJ,  and  from  the  pencil  to  major 
pin  the  distance  HC,  now  trace  the  curve  through  the  points  C, 
J" and  A  for  the  center  line  of  rail  on  mould,  repeat  the  operation 
for  the  concave  and  convex  curves  of  mould;  2'^  of  straight  wood 
is  added  on  at  D  to  help  the  easing  at  the  joint  connecting  the 
straight  rail. 

At  sections  L  and  M  the  bevels  are  shown  applied  to  cross 
the  tangents;  the  bevels  shown  in  the  angles  8  and  9,  Fig.  8  are 
applied  at  sections  ilf  and  L,  respectively. 

If  a  trammel  be  not  at  hand,  then  bisect  the  chords  and  use 
ordinates  as  previously  described,  BC  will  be  the  director  on 
face-mould,  and  DE  will  be  the  director  on  plan,  Fig.  7. 

For  the  face-mould,  Fig.  9,  the  diagonal  will  be  the  director, 
both  on  the  mould  and  on  plan,  because  both  tangents  have  the 
same  inclination. 

At  N,  Fig.  3,  observe  the  tangent  NS  is  drawn  with  the  same 
inclination  as  the  straight  rail,  thus  lifting  tlie  falling  line  of  rail 
at  the  upper  end  of  winders;  if  kept  down  at  tliis  point,  and  a 
short  easing  made  to  connect  the  wreath  rail,  the  wreath  would  be 
improved  and  be  still  high  enough;  it  is  thouglit  well  to  show  the 
langents  in  elevation  in  this  way,  so  as  to  develop  a  face-mould 
having  the  minor  axis  outside  the  mould  and  near  the  .ioint,  and 
thus  exhibit  an  extreme  in  hand-railing,  in  a  practical  way;  for  in 
practice  the  stair-builder  has  various  shapes  of  moulds  to  make, 
and  how  to  construct  and  prove  their  correctness  is  the  aim  here 
sought. 


PLATE  44. 

Plate  44.  Exhibits  the  construction  of  face-moulds  for  a 
flkjht  of  ijcometrlcal  stairs  circular  on  plan  and  starting  from  a 
newel. 

Fig.  1.     [Scale  H^'—'^  foot.]     Shows  the  plan. 

The  regular  tread  equals  10^'''  by  6%''''  rise;  they  are  spaced 
off  on  the  regular  tread  line  18  inches  from  the  outer  string,  the 
corners  remaining  square  to  give  more  room,  and  by  using  a  wall 
rail  will  suit  the  ascent  and  descent  of  old  people  better  than  if 
the  wall  string  were  concentric  with  tlie  outer  string.  For  effect, 
in  grand  circular  stairways  the  wall  string  should  lie  circular  to 
correspond  with  the  front  string,  and  the  wall  space  ornamented 
with  niches  for  statuary.  The  rail  is  4^^  wide  by  h'^  deep,  to  be 
double  moulded. 

Pig.  2.     [Scale  %^''==1  foot.]     Sliows  phtn  of  tangents. 

The  radius  for  the  cylinder  equals  1.5^^,  and  the  balusters  are 
2^^  by  2''^,  and  by  allowing  }i^^  for  the  projection  of  bracket,  the 
radius  for  the  center  line  of  rail  will  equal  15%^''.  At  the  newel 
the  cylinder  is  contracted,  which  increases  the  length  of  first  step 


Pr.ATK  44.  199 

and  make  the  stairs  more  inviting  to  ascend.  Tlie  direction  of 
risers  and  tlireads  are  given  on  plan;  tlie  widtli  of  rail  (4'''')  is  laid 
ott"  on  plan,  so  that  ordinates  may  be  used  in  drawing  the  face- 
moulds.  The  plan  of  rail  is  divided  into  live  wreath-pieces;  the 
chord  of  the  segments  for  Nos.  3,  3,  4  and  5  wreatli-pieces  equals 
the  radius  OB:  tlie  joints  shown  at  A,  B,  C  and  D  all  radiate 
to  the  center  0/  the  joint  at  E  shows  2^^  of  straight  wood  added 
to  connect  the  straight  rail  on  the  level. 

Draw  the  tangent  FH  perpendicular  to  radius  F^,  and  tan- 
gents AH,  AJ,  BJ,  BK,  CK.  CL,  DL,  DM  aud  EM,  all  per- 
pendicular to  the  joints  A,  B,  C,  D  and  E;  parallel  with  the 
tangents  iZlFand  HA,  draw  FN  and  AN;  parallel  with  tangents 
AJ  and  BJ,  draw  BP  and  AP,  forming  the  parallelogram 
AJBP  on  plan.  The  parallelograms  for  Nos.  .3,  4  aud  5  are  the 
same,  because  the  chords  BC,  CD,  DE,  are  of  one  length. 

From  F  No.  1  and  perpendicular  to  tangent  AH,  draw  FG\ 
from  A  No.  3,  and  at  right  angles  to  BJ  prolonged,  draw  AS; 
from  C  No.  4,  and  pei-pendicular  to  tangent  DL  prolonged,  draw 
CT;  from  D  No.  5,  and  perpendicular  to  tangent  EM  prolong- 
ed, draw  DU. 

The  treads,  risers,  joints  of  rail  and  tangents  on  plan  being 
located,  we  are  ready  to  draw  the  increased  length  of  tangents 
in  elevation. 

Pig.  3.  Exhibits  the  elevation  of  tojiigents,  treads  and 
risers,  as  developed  from  tangents  on  plan  Fig.  2,  for  the  in- 
creased length  of  tangents  for  the  face-moulds. 

To  economize  room,  first  find  the  average  pitch  on  the  line 
of  tangents;  then  elevate  the  treads  and  risers  from  the  tangents 
on  plan.  The  stretchout  of  tangents  from  F  io  M  equals,  we 
will  say,  943^^''  which  being  divided  by  14  (the  number  of  risers) 
equals  say  6%  ^''  for  the  average  tread;  then  set  a  bevel  to  the  average 
pitch,  Q%^'  by  Q%^'  rise,  and  draw  the  perpendiculars  F,  H,  A, 
J,  B,  K,  C,  L,  D.  Jf  and  E.  Now  elevate  Nos.  1  to  15  treads 
and  risers  from  the  tangents  on  plan  Fig.  2;  then  determine 
which  tangents  will  be  level.  Tangent  FH  connects  the  newel 
cap,  and  should  be  level,  or  nearly  so,  k)  make  the  curve  connect- 
ing the  cap  graceful  as  possible,  we  will  give  the  tangent  HF'No. 
1  a  slight  inclination,  and  by  forcing  the  curve  at  the  miter  joint, 
a  more  graceful  curve  will  be  obtained  than  if  the  tangent  HF 
in  elevation  was  to  remain  level.  Again,  tangent  ME,  at  the 
lauding,  should  be  level,  for  a  full  easing  at  that  point  is  re- 
quired. 

From  the  top  of  No.  1  step  set  up  to  F,  the  height  to  under- 
side of  rail,  5'^  plus  the  half  depth  of  rail  [2^^^],  equals  7K''; 
at  the  landing  set  up  to  E,  i''  to  the  underside  of  rail,  plus  the 
half  depth  of  rail  f3K'^]  equals  ^H"  to  the  center  of  rail  at  E: 
draw  EM  at  right  angles  to  the  spring  line  E;  now  M  and  H  are 
fixed  points;  from  the  external  angle  of  Nos.  4  and  12  rise,  draw 
arcs  equal  to  the  half  depth  of  rail  \2yi"\  and  draw  the  inclina- 
tion of  tangents,  cutting  the  perpendicular  at  H,  A,  J,  B,  K,  C, 
and  L;  now  L  and  M  are  fixed  points,  draw  ML  prolonged  to 
cut  the  perpendicular  C  at  N;  draw  FH  prolonged,  cutting  the 
perpendicular  A  at  D;  from  F  draw  the  horizontal  line  FO, 
cutting  the  perpendicular  H  at  P,  and  also  cutting  the  tangent 
AH" prolonged  at  y;  draw  AQ  at  right  angles  to  AO,  cutting  the 
perpendicular  J"  at  JZ;  draw  BS  at  right  angles  to  BQ,  cutting 
the  perpendicular  K  at  T;  draw  CU  square  to  CS,  cutting  the 
perpendicular  L  at  v;  from  D,  and  at  right  angles  to  DU,  draw 
DiV,  cutting  the  perpendiculars  M  aud  L  9.1  X  aud  Z,  and 
Riso  cutting  the  tangent  CL  prolonged  at  J, 


200  Plate  44.  ~~' 

Now  OA  is  the  hckiht  for  No.  1  wreath-piece;  13 Q  ami  CS 
are  the  hcMjlds  for  Nos,  3  and  3  wreath-piece,  they  beiiij?  botli  the- 
same.  DJJ  is  the  heujht  for  No.  4  wreatli-piece,  and  XJkZ"  tlic 
hcUiht  for  No.  5  wreatli-piece.  Malce  Oa  equal  tlie  cliord  FA  on 
plan;  prolong  (JA  to  the  right  and  make  Ab  equal  the  diagonal 
NH on  plan;  malte  Qd  equal  the  chord  BA  No.  3  on  plan;  make  Ui 
and  Wiif  equal  the  chords  DC  and  DE  Nos.  4  and  5  on  plan. 
Fig.  3;  make  Pni  equal  GH  No.  1  on  plan.  Fig.  2;  let  Rn  equal  JS 
No.  3  on  plan;  make  Vt  and  Z-j  equal  iT  No.  4  on  plan;  let  Mg 
equal  UM  No.  .5  on  plan,  Fig.  3.  From  the  points  rti,  ii,  t,  c 
and  g,  draw  Jiie,  i27i,  ti,  CP  and  ^/S  square  to  the  tangents  AH, 
J  A,  DL,  CL  and  DM  produced. 

Bevels.*  Return  to  plan,  Fig.  3,  make  HV  No.  1  equal 
Py,  Fig.  li,  draw  VF  indefinite  for  the  director;  from  A,  and 
perpendicular  to  FV,  draw  AW;  make  Wa  equal  OA,  Fig.  3; 
join  Aa,  and  in  the  angle  at  a  tlie  bevel  is  found  for  the  joint  F, 
at  the  miter  cap;  for  the  joint  at  A  on  No.  1  wreath-piece,  makt? 
GrJC  equal  me,  Fig.  3;  join  XF,  and  in  the  angle  X  is  found  the 
bevel  as  shown. 

For  Nos.  3  and  3  wreath-piece,  make  Sy  equal  nh,  Fig.  3; 
join  yA  for  the  bevel  required  for  the  two  wreath-iiieces  on  each 
joint;  for  No.  4  wreath-piece,  make  Tb  equal  CP,  Fig.  3,  and 
Td  equal  tl,  Fig,  3;  join  be  and  dc,  and  in  the  angle  b  is  found 
the  bevel  for  the  joint  at  C,  and  the  bevel  shown  at  d  applies  at 
joint  marked  D;  for  No.  5  wreath-piece,  make  Uni  eiiual  gS. 
Fig.  3;  make  Un  equal  the  height  XM,  Fig,  3;  connect  mD  and 
i2l>  and  the  angle  at  m  gives  the  bevel  for  the  joint  at  D,  and  the 
angle  at  n  gives  the  bevel  for  the  upper  joint  at  E. 

Now  draw  the  half  width  of  rail  [3^^]  parallel  with  the  tan- 
gents to  cut  the  hypothenuso  of  triangles  forming  the  bevels;  for 
No.  1  wreath-piece  tlie  dotted  line  cuts  at  3  and  3,  and  for  Nos.  3 
and  3  wreath-piece  the  dotted  line  cuts  at  4;  for  No.  4  wreath- 
piece  the  dotted  line  cuts  at  .^)  and  6,  and*it  No.  .5  wreath-piece 
the  dotted  line  cuts  at  7  and  8. 

Pace-moulds,  Fhj.  4  shows  the  faee-monhl  for  No.  1 
torailh-inece,  fttortlng  from  the  newel  post. 

Make  AH  equal  AH,  Fig.  3;  with  A  as  a  center,  and  Aa, 
Fig.  3,  for  a  radius,  draw  arc  at  F;  with  iJas  a  center,  and  HF. 
Fig.  3,  for  a  radius,  draw  arc  intersecting  at  F;  draw  HF  pro- 
longed, parallel  with  HA  and  HF,  draw  FN  ami  AN,  for  the 
parallelogram  NAHF,  on  the  cutting  plane. 

Proof.  The  diagonal  HN  must  equal  the  distance  Db,  Fig. 
3;  if  so,  the  parallelogram  is  correct. 

Make  Hy  equal  Hy,  Fig.  3.  Connect  yF  for  the  director  on 
face-mould.  Draw  F  3  indefinite,  and  at  right  angles  to  Fy. 
Make  joint  at  A  at  right  angles  to  AH.  Make  F2  and  F  3,  each 
equal  a  3,  Fig.  3.  Make  A  4  and  A  .5,  each  equal  X  3,  Fig,  3. 
Draw  the  chord  AF.  Bisect  the  chord  AF  at  3;  bisect  BA  and 
BFai  D  and  C;  from  the  points  A,  D,  B  and  C,  draw  ordinatcs 
parallel  with  the  director  jy,-  now  on  plan,  at  No.  1,  bisect  AF 
at  B;  bisect  BA  and  BF  at  D  and  C. 

From  the  points  A,  D,  B,  C  and  F,  draw  ordinates  parallel 
with  the  director  FV,  to  cut  the  concave,  convex  and  center  line 


'■>  *In  practice,  a  sood  plan  is  to  take  the  bevels  off  the  drawing 
on  to  a  piece  of  1)oard,  and  liaii,;,'  up  until  needed,  tlien  the  drawmg 
board  can  be  laid  away.  To  take  an  angle  from  the  drawing  with  a 
bevel,  first  lay  down  the  steel  square  to  one  of  the  lines,  then  adjust 
the  bevel  from  the  square  to  the  other  liue. 


Plate  44.  20-1 

of  rail  on  plan;  then  transfer  the  points  on  the  ordinates  from  the 
plan  Fig.  3  to  corresponding  ordinates  on  face-mould  Fig.  4,  and 
trace  the  curves  through  the  points,  using  a  flexible  strip.  At  F 
add  on  1%"  for  miter  on  the  line  of  tangent  HF,  but  make  tlu; 
.splice  joint  at  right  angles  to  tlie  director  Fy,  instead  of  the 
tangent  HF,  as  is  done  for  a  butt  joint;  by  drawing  the  joint  at 
right  angles  to  the  director  Fy,  the  joint  will  be  plumb  when  the 
wreath-piece  is  elevated  into  position,  and  at  the  same  time  will 
be  square  to  the  face  of  plank,  because  the  joint  is  parallel  to 
the  major  axis. 

Observe  in  this  case  the  joint  made  from  the  director  cuts 
tlie  rail  oblique  at  F,  on  plan  Fig.  3,  and  not  normal  to  tiie  curve, 
as  it  would  if  drawn  at  right  angles  to  the  tangent  HF,  Fig.  2; 
hence  the  block  pattern  must  be  increased  in  width  equal  to  the 
oblique  cut  at  this  joint. 

The  sections  M  and  JVshow  the  be^'els  api»lied  through  the 
center  of  plank;  they  cross  the  tangents  in  their  application. 
The  block  pattern  is  applied  square  to  the  lines  made  from  tlie 
b«vels;  the  shaded  parts  show  the  thickness  of  plank  and  the 
amount  of  overwood  to  be  taken  oft". 

Fig.  5.  Shows  tlie  face-mould  for  Nos.  2  and  3  wreath- 
piece. 

Make  BJ  equal  the  tangent  BJ,  Fig.  3;  with  B  for  a  center 
and  Bd,  Fig.  3,  as  a  radius,  draw  arc  at  A;  then  with  J"  for  a 
center  and  JB  as  a  radius,  draw  arc  intersecting  at  A,  join  AJ; 
parallel  with  JB  and  JA  draw  AP  and  BP.  Then  PBJA  will 
be  the  parallelogram  on  the  cutting  plane. 

Proof.  The  diagonal  JP  nuist  e(iual  the  diagonal  JP  on 
plan  Fig.  2.  Make  joints  at  A  and  B  perpendicular  to  tlie  tan- 
gents BJ  and  AJ;  as  both  tangents  are  of  eiiual  length,  the 
diagonal  JIP  becomes  the  director  on  the  face-mould,  and  also  on 
plan  Fig.  a.  Draw  the  chord  AB  on  mould  and  also  on  plan; 
bisect  them  at  CF  and  D.  Draw  the  ordinates  parallel  with  the 
directors  J'J'at  Fig.  5,  and  also  on  phm  Fig.  2;  then  transfer  the 
distances  from  the  plan  Fig.  2,  to  the  face-mould.  Fig.  5,  using 
chords  for  base  line-;  make  A  2,  A  3,  and  B  i,  B  5.  each  equal 
yi,  Fig.  2.  Now  trace  the  curve  through  the  points  for  the  con- 
cave and  convex  sides  of  mould.        ' 

If  a,  trammel  or  rod  is  desired  in  i)i'ofereneo  to  tiic  ordinates,  (.hen 
extend  the  diagonal  JP  iudelinite;  make  PO  equul  to  the  di;i;j;onal  J/' 
in  lliis  ease.  From  the  points  2,  3,  4,  5,  draw  lines  indefinite,  and 
at  riiilit  a.nirles  to  the  joiuts;  from  O,  di'aw  the.  radial  lines  OI> 
and  <>A,  indefinite,  which  gives  the  points  of  cotitaet,  as  G,  7,  8,  9 
on  the  j-adi-'.l  lines;  at  rij^'iit  angles  to  OJ  draw  UK,  to  indieiite  tlie 
tranunel  and  uss  the  rod,  malving  points,  througli  which  draw  tiie 
elliptic  curves,  using  a  pliable  strip. 

The  sections  at  M  find  N  sliow  the  bevel  at  y,  No.  2,  Fig. 

2,  applied  through  the  center  of  plank;  observe  they  cross  the 
tangents. 

Fig.  6.  Exhibits  the  facc-nwidd  for  No.  4  ivr calh-piccc 
on  plan. 

Make  CLI  equal  CLI,  at  No.  4,  in  elevation,  Fig.  3.  Witii 
Cas  a  center,  and  Z>/,  Fig.  3,  for  a  radius,  draw  arc  at  D;  with 
Zf  as  a  center,  and  tangent  LD,  Fig.  3,  for  a  radius,  drav/  arc 
iidersccting  at  D,  Connect  LD;  jiarallel  with  DL  ami  CL,  draw 
CQ  luid  DQ  for  the  parallelogram  QDLC,  on  tiie  cutting  plane, 
or  plane  of  plank.  < 

"   Proof.     The  diagonal  LQ  must  equal  the  distance  VN,  Fig. 

3.  Make  joints  at  D  and  C  square  to  the  tangents  DL  and  CL, 


203  Plate  44. 

join  D/for  the  director;  make  B  8  and  D  9  each  equal  D  5  No.  4 
on  plan,  Fis-  2;  malie  C4,  C5  each  equal  h  G  No.  4  on  plan;  now 
draw  the  chord  line  DC.  Fig.  6,  also  on  plan,  Fig.  2;  make  LI, 
Fig.  2  equal  Zi,  Fig.  3,  draw  ID  for  the  director  on  plan.  Bisect 
the  chords  as  previously  explained,  and  draw  tlie  ordinates  parallel 
with  the  directing  ordinate  DI  to  cut  the  inside,  center  and  out- 
side of  rail  on  plan,  Fig.  2;  now  transfer  the  points  on  the  ordinates 
on  plan  at  No.  4,  Fig.  2,  to  corresponding  ordinates,  Fig.  6,  using 
the  chords  as  base  lines,  then  trace  the  elliptic  curves  through  the 
points  shown.  If  a  trammel  or  rod  be  i)reterred,  then  prolong  the 
diagonal  LQ  indefinite,  make  Qo  equal  LiQ;  from  O,  draw  the 
radial  lines  OC  and  OD  indefinite;  at  right  angles  to  the  joints, 
draw  3  2  and  9  3,  also  4  6  and  5  7  for  the  points  of  contact;  draw 
OA  parallel  to  1?J and  equal  to  the  radius  OS  on  plan,  for  the 
semi  minor  axis;  draw  the  direction  of  nuijnr  axis  through  O  and 
at  right  angles  to  OA;  make  AF  aiul  AB  each  equal  the  half 
width  of  rail  [2^^];  now  with  a  rod,  find  points  in  the  elliptic  curve, 
through  which  trace  the  curves  using  a  pliable  strip. 

The  sections  T  and  S  show  the  bevels  applied  through  the 
center  of  plank,  so  as  to  cross  the  tangents;  the  shaded  parts  indi- 
cate the  thickness  of  plank  and  alt-o  the  width  at  the  joints  to 
saw  out  the  crooks  from  the  plank;  at  the  minor  axis,  14"  or  less 
is  all  that  will  be  required  over  the  true  width  of  rail,  to  allow  for 
the  twist  of  rail. 

Fig.  7.  Exhibits  the  face^iouhl  fur  Xo.  5  wrcath-imcc  on 
plan. 

Make  tangent  i)ikr  equal  DM,  Fig.  3.  With  jD  as  a  ceuter, 
and  Eh,  Fig.  3  for  a  radius,  draw  arc  at  E;  with  Jlf  as  a  center, 
and  EM,  Fig.  3  for  a  radius,  draw  arc  intersecting  at  E,  draw 
tangent  ME,  which  becomes  the  director,  make  joints  at  M  aud 
E  perpendicular  to  the  tangents;  at  E,  2"  of  straight  wood  is 
added  on  to  help  the  easing  connecting  the  straiglit  rail  on  tlie 
level;  parallel  witli  tangents  MD  and  ME,  draw  SR  and  DR 
for  the  parallelogram  RDME o\\  the  eutting  plane. 

Proof.  The  diagonal  MR  must  equal  the  distance  EX, 
No.  5,  Fig.  3  ;  make  D  2  and  D  3,  each  equal  m  8.  at  No. 
5,  Fig.  2.  Make  E  4  and  E  5,  each  equal  n  7,  at  No.  .5 
Fisr.  2.  Draw  chord  DE;  bisect  the  same  at  A,  also  bisect 
AD  and  AE  at  C  and  B;  now  ]>arallel  with  the  direc- 
tor, draw  ordinates  iudefiinite.  Bisect  the  chord  DE,  on 
plan,  Fig.  2,  in  like  manner,  and  draw  ordinates  parallel  with  the 
director  ME,  to  cut  the  concave,  center  and  convex  sides  of  rail; 
now  transfer  the  points  on  the  ordinates  at  No.  5,  Fig.  2,  to 
corresponding  ordinates  on  face-mould.  Fig.  7,  using  the  chord 
lines  DE  as  a  base;  now  trace  the  curves  through  the  points, 
using  a  pliable  strip. 

The  sections  Wand  y,  show  the  bevels  applied  through  the 
center  of  plank;  the  shaded  parts  show  the  thickness  of  ])lauk, 
and  also  the  width  at  the  joints  to  saw  out  the  crooks  from  the 
plank;  observe  the  bevels  do  not  cross  the  tangents  in  this  case. 

If  a  trannnel  be  preferred  to  the  onlinaies,  then  prolong  the 
diagonal  MR,  and  also  tlie  joint  line  5  E  4,  to  inter.sect  at  O, 
then  OE  wiil  be  the  scnii-major  axis;  the  senii-iuinor  axis  will  be 
at  right  angles  and  ecjual  to  the  radius  EO,  Fig.  3,  {lo^i"). 
Draw  the  radial  line  OD  prolonged;  at  right  angles  to  the  joint, 
draw  2  7  and  3  6  for  the  points  of  taugency. 

Proof.  RO  must  equal  MR  in  this  case.  The  ordinates, 
however,  wiil  be  found  more  convenient,  as  less  space  will  be 
required  in  the  construction  of  the  moulds.  t- 


Plate  45.  203 

Balusters.  If  the  length  of  odd  balusters  be  required 
under  the  tangent  in  elevation,  Fig.  8;  the  directors  on  plan.  Fig, 
2,  for  each  wreath  piece  will  give  their  location  on  the  tangents, 
and  may  be  transferred  to  their  position  in  elevation  as  previ- 
ously described. 

Self-Supporting  Stairs. 

Self-supporting  stairs  circular  on  plan  may  be  constructed  in 
several  ways.  The  main  object  is  to  have  them  secure  at  the  land- 
ing and  at  the  starting  with  a  substantial  system  of  carriage  under- 
neath the  steps.  The  string  for  tlie  concave  side  sliould  he  made 
from  lYz"  plank,  and  dadoed  on  the  bade;  then  bent  over  a  drum  and 
keyed  with  hard  wood  li:eys  set  in  glue.  The  string  for  the  convex 
side  should  be  dadoetl  and  keyed  in  the  same  manner,  and  after 
being  set  in  place  a  thin  veneer  may  be  bent  over  the  same  to  cover 
the  keys  and  joints.  The  steps  and  risers  may  be  constructed  in  the 
usual  way,  all  laid  off  from  the  working  plan,  which  is  drawn  full 
size  on  the  floor  or  large  drawing  board,  ^\hen  the  stairs  are  to  be 
set  up  in  tlie  building  they  should  be  lined  off  on  the  door,  and  the 
strings  and  risers  set  plumb  over  their  lines  on  the  floor.  The  string 
for  the  concave  side  should  l)e  set  first  and  fastened  to  the  joist 
above  and  floor  below,  and  supported  temporarily  between  by  setting 
up  several  scantling  and  screwing  them  to  the  face  of  string.  The.se 
scantling  should  be  well  braced,  holding  the  string  rigid  and  plumb 
over  the  lines  on  the  floor. 

Now  the  string  for  the  convex  side  may  be  set  up  true  to  the  lines 
on  the  floor,  and  supported  temporarily  in  the  same  manner,  as  the 
concave  string.  Fhice  the  supports  at  the  face  of  string,  and  brace 
them  well  to  hold  the  string  firm  and  true  to  the  lines  on  floor.  The 
steps  and  risers,  being  tongued  blocked  and  all  well  glued,  may 
now  be  set  in  place.  Then  take  strips  ^2"  thick  and  3"  or  i"  wide,  glue 
and  nail  them  with  the  .3"  way  in  a  vertical  position  to  the  back  of 
the  concave  string,  extending  them  down  into  the  joist  at  the  start- 
ing, and  also  up  into  the  joist  at  the  landing.  Keep  the  strips  up  to 
line  with  the  under  edge  of  risers;  then  the  sotHt  will  be  regular. 
At  intervals  cut  in  brackets  underneath  each  step,  having  the 
grain  perpendicular  to  the  tread.  These  brackets  are  nailed  to 
the  laminated  soffit,  and  triangular  blocks  maj'  be  glued  and  nailed 
to  the  step,  and  also  the  bracket.  After  tlie  soffit  is  covered  in  this 
way  then  strip  for  plastering,  or  a  better  way  is  to  panel  the  soffit  with 
Lincrusta  Walton.  Iron  bolts  should  be  placed  across  the  stairs  par- 
allel with  and  at  the  bade  of  every  otlier  rise;  at  the  starting  a 
spandrel  should  fill  the  triangular  space  to  four  feet  high,  which  will 
give  additional  strength.  At  the  landing  two  by  half-inch  flat  iron 
L2"X'/2"j  shiuldbelet  into  the  joist  and  soffit  03  stairs  where  the  soffit 
of  stairs  ease  olT  to  to  »he  level.  These  irons  should  be  well  bolted 
tx)  thesam*.  . 


PLATE  45. 

Plate  45.     E.rMblts  the  conatructlon  of  the  face-mould  for 
a  st(tir-casc  eUlptical  on  plan,  and  staHing  from  a  scroll. 
Fig.  1.     [Scale  ?X^'=1  foot  ]     Shows  the  plan. 

The  direction  of  risers  in  an  elliptical  stairs  should  be  normal 
to  the  curve,  or  near  to  that  as  possible,  so  the  rail  may  be  con- 
structed more  readily  to  an  even  height  for  the  hand,  and  at  the 
same  time  obtain  easy  flowing  and  graceful  curves;  and  if  the 
front  string  bo  open,  having  return  nosings  and  brackets,  long 
miters  on  the  return  nosings  will  be  avoided;  or  should  tlio  outer 
string  be  close,  the  nosings  and  string  lines  will  show  more  even, 
and  a  more  satisfactory  job  will  be  the  result,  and  the  angles  of 
strings  and  risers  will  be  less  liable  to  collect  the  dust.  Observe 
No.  16  tread  is  increased  in  width  to  receive  two  balusters,  and 
thus  allowing  the  rail  tocase  oft'  gracefully  at  the  landing.  The  con- 
struction of  such  stairs  requires  the  skill  of  a  practical  stair-builder. 

In  the  construction  of  the  wall  string,  dado  the  back  of  string 
parallel  with  risers.  Bend  over  a  drum  and  insert  dry,  hard  wood 
keys,  well  glued.  A  joint  may  lie  made  at  the  center,  and  the  drum 
m.'ide  high  enough  to  take  in  No.  10  rise.  Then  both  the  upper  and 
lower  pieces  may'be  bent  over  the  same  drum  l)y  turning  the  notched 


204  Plate  45. 

edges  toward  each  other,  and  thus  save  room  and  material.  The 
outer  striiis  may  be  made  in  the  same  way;  if  for  a  close  string, 
while  on  the  drum  lag  out  to  the  required  thickness  to  admit  the 
veneer  on  the  convex  side.  Then  house  in  the  treads  and  risers; 
cross- tongue  and  bolt  the  joints  of  string  if  made  in  two  pieces; 
light,  thin  mouldings  may  be  easily  bent  and  nailed  to  place;  or  if 
large  and  lieavy  mouldings  for  panels;  they  should  be  worl<;ed  from 
the  solid  plank  for  flrst-class  worlc.  If  large  mouldings  are  used  as 
string  mouldings,  tlien  work  each  member  out  sep;irately  and  nail 
tliem  to  place.  A  little  ingenuity  displayed  in  this  line  will  avoid  the 
kerling  of  mouldings,  wliich  should  never  be  done,  particularly  when 
the  finish  is  in  hard  wood.  In  splicing  winders  or  steps  plough  and 
xise  slip  tongues  cut  across  the  grain  obliquely,  and  of  very  dry 
iiiaterial;  beads  may  be  steamed  and  bent  to  plaoe;  if  large,  they 
will  require  to  be  nailed  every  few  inches.  Tlie  steaming  of  light 
v.ood  discolors  the  g'rain,  and  should  be  avoided  for  liard  wood 
finish,  unless  of  walnut,  which  being  a  darlv  wood,  the  steaming  is 
not  objcctionalile. 

For  intenmdiate  rails  between  the  string  and  hand  rail,  which 
is  intended  to  support  balusters  or  panels  of  spindle  woj'li;  these 
intermediate  rails  nuiy  be  laminated  in  several  thiclcnesses  of 
strips  by  clamping  and  gluing  three  or  four  pieces  at  a  time;  over 
the  drum  the  strips  sliould  be  tiiin  enough  to  bend  easily,  the 
clamps  may  be  constructed  on  the  drum,  and  wedges  used  every 
few  inches;  paper  should  be  laid  over  tlie  drum  before  gluing,  to 
prevent  the  work  adhering  to  the  drum;  string  mouldings  may 
be  built  up  in  the  same  manner,  and  worl<ed  after  being  removed 
from  the  drum.  If  heavy  paneling  be  required,  the  drum  will 
answer  for  a  form  over  which  the  paneling  may  be  constructed. 

Fig.  2.     [Scale  M"=l  foot.]     Shows  tlie  plan. 

The  dotted  line  CDJEFG  sliows  the  center  line  of  rail, 
which  is  a  true  ellipsis;  tlie  parallel  lines  show  tlie  width  of  rail. 
Joints  are  shown  at  A,  B,  C,  U,  E,  F  and  G,  they  are  drawn 
normal  to  the  center  line  ";  at  riy;lit  anijles  to  the  joints,  draw 
the  tangents  AH  and  BH,  BJ  and  CJ,  CK  and  DK,  DL  an  i 
EL,  EMawA.  FM,  FN  and  GN,  at  G;  two  or  more  inches  of 
straight  wood  is  added  on  to  connect  the  straight  rail;  parallel 
with  the  tangents,  draw  lines  from  joints  to  form  the  parallelo- 
gram on  plan. 

OAHB  shows  the  ]iarallelogram  for  No.  1  wreath-piece  on 
plan;  PBJC  the  parallelogram  for  No.  2  v.reath-piece;  QCKD 
for  No.  :]  wreath-piece:  RDLE  for  No.  4;  SEMF  for  No.  5,  and 
TFNG  shows  the  parallelogram  for  No.  6  Viieath-piece. 

From  C  and  perpendicular  to  DK  prolonged,  draw  CU:  from 
D  and  at  right  angles  to  tangent  CK  prolonged,  draw  DVfor 
No.  3;  at  No.  4  draw  EW  perpendici-iar  to  tangent  DL  pro- 
longed; at  No.  6  draw  FX  at  right  angles  to  tangent  GN  pro- 
longed. The  joints  and  tangents  being  now  lined  olf  on  plan, 
next  proceed  to  unfold  the  tangents  from  plan,  and  elevate  the 
treads  and  risers  to  determine  the  increased  length  of  tangents  in 
elevation. 

Fig.  3.    E.rhihUs  the  clcvntion  of  tangents. 

First  find  the  average  pitch  on  the  line  of  tangents,  as  directed 
at  the  preceding  plate,  to  which  set  a  bevel,  and  draw  the  per- 
pendiculars A,  H,  JB,  J,  C,  Ky  6iQ.,  fiom  the  edge  of  drawing 
board.  The  horizontal  distance  apart  corresponds  to  those  on 
plan;  next  elevate  the  treads  and  riseis  from  the  tangents  on  plan 
Fig.  2.  They  will  all  be  square  and  parallel  to  the  peniendiculars. 
The  perpendicular  A  indicates  a  joint,  aiul  H  an  angle;  B  a 
joint,  and  J" an  angle;  Ca  joint  and  K  m\  angle;  D  a  joint,  and 
L  an  angle;  E  a  joint,  and  if  an  angle;  F  a  joint,  and  N  an  angle; 
and  G  a  joint  at  the  landing. 

*See  Plate  5,  Fig.  8,  how  to  draw  a  line  noi'mal  to  an  elliptical 
curve. 


Pl,ATK   i').  SfilS 

To  g;ive  the  scroll  a  graceful  cun'e,  set  up  1-"  from  the  top 
of  No.  1  step  to  the  imcUn-  side  of  rail,  phis  IM^^  to  A  for  the 
center  of  rail  (2M^^);  fvt  right  angles  to  the  perpendicular  A, 
draw  AH":  then  if  is  a  fixed  point.  From  the  floor  line  at  the 
landing  set  up  4"  to  the  xuuler  side  of  rail,  plus  IM'^  to  the  cen- 
ter of  rail  at  G  (4^^+lK^^=5K''0=5K'^:  di'aw  GJV square  to  the 
perpendicular;  theu  N  is  another  fixed  point.  From  the  external 
angle  of  Xos.  7  and  12  tread  draw  arc  to  IH'^  radius;  then  draw 
the  inclination  for  the  center  of  rail  to  tangent  the  arcs,  and  cut- 
ting the  perpendiculars  at  M,  E,  L,  D  and  K.  Theu  M  and  K 
also  becrime  fixed  points;  connect  NM,  cutting  the  perpendicular 
at  J'.  From  if  draw  iTJ.  cutting  the  perpendicular  at  C  Join 
JH,  cutting  the  perpendicular  at  B;  from  the  point  H  the  tan- 
gents should  be  drawn  so  as  to  give  a  gradual  rise  to  the  rail. 

As  stated  elsewhere,  the  location  of  tangents  is  discretionary 
with  the  stair-builder;  the  higher  they  are  raised  above  the  treads, 
the  rail  will  be  correspondingly  raised;  if  the  rail  be  a  little  high 
the  fault  will  not  condemn  the  work,  but  on  the  other  hand,  if 
too  low,  theu  serious  objections  may  be  urged.  The  young  man 
will  learn  with  a  little  practice.  The  direction  of  tangents  should 
be  drawn  so  as  to  give  the  rail  as  easy  flowing  curves  as  the  plan 
will  admit  of. 

From  H,  and  square  to  perpendicular  B  draw  HO:  then 
OB  will  be  the  hcUjht  for  No.  1  wreath-piece.  From  B,  and 
square  to  perpendicular  C,  draw  BP,  cutting  perpendicular  J  at 
Q;  then  PC  is  the  height  for  No.  2  wreath-piece.  From  C,  and 
at  right  angles  to  perpendicular  D,  draw  CR,  cutting  perpendicu- 
lar K  at  S;  then  DR  is  the  height  for  No.  3  wreath-piece.     From 

D,  and  square  to  perpendicular  E,  draw  I>T,  cutting  perpendicu- 
lar L  at  U;  then  TE'is  the  height  for  No.  4  wreath-piece.     From 

E,  and  scjuare  to  perpendicular  F,  draw  E,  NN;  then  NN,  F  is 
the  hcUjht  for  No.  5  wreath-piece.  From  F,  aud  square  to  per- 
pendicular G.  draw  FW,  cutting  perpendicular  N  at  X;  tlu'u 
WG  will  be  the  hckiht  for  No.  (5  wreath-piece. 

It  will  be  observed  that  the  tangents  EM  and  MF  for  No.  5 
wreath-piece  are  the  same  length,  and  also  height  as  for  No.  3 
wreath-piece,  and  need  not  be  described  further,  as  the  face- 
mould  and  bevels  for  No.  3  will  apply  to  No.  5  wreath-piece;  for 
by  turning  No.  3  wreath-piece  upside  down  it  will  answer  for  No.  ri. 

Prolong  the  tangent  CJ"  to  intersect  BQ  at  a;  extend  tan- 
gent JB  J"  to  intersect  PC  at  b:  prolong  tangent  DK  to  intersect 
CS  at  d:  prolong  tangent  CK  to  intersect  DR  at  e.  Make  of 
equal  the  chord  AB.  Fig.  2;  let  Pg-and  Ck'^o.  2  equal  the  chord 
BC,  Fig.  3;  make  J^ii  equal  the  chord  CD,  Fig.  2;  make  2Vcqual 
the  chord  DE,  Fig.  2;  let  Win  equal  the  chord  FG,  Fig.  2,  and 
Wl  equal  the  diagonal  NT,  Fig,  2;  make  Dn  equal  the  diagonal 
MSov  KQ,  Fig.  2. 

Make  SP  equal  KIT,  on  plan.  Fig.  2,  Let  kr  equal  KV, 
Fig.  2.  Make  uq  equal  Z/W on  plan,  Fig.  2.  Let  Ns  equal  Njr, 
on  plan.  Fig.  2.  From  Q,  No.  2  and  square  to  CJ,  draw  Qt:  from 
XX,  and  square  to  tangent  BJ  prolonged,  draw  XX  Z;  from 
p,  and  square  to  tangent  DK  prolonged,  draw  pv;  from  r,  and 
square  to  tangent  CK  prolonged,  draw  i',  00;  from  q,  and 
square  to  tangent  DL,  draw  qw;  from  S,  and  square  to  tangent 
P2V  prolonged,  draw  Sy- 

Parallel  with  JQ,  draw  the  half  width  of  rail  (2^0  >  cutting 
the  tangents  SJ"and  CJ"  prolonged,  at  IS  and  20. 

Bevels.  Now  return  to  plan,  Fig.  2,  and  draw  the  bevels 
aud  the  increased  width  of  face-moulds  at  the  joints.     Make  Ja 


206  Plate  45. 

No.  2  equal  Qt,  Fig.  3.  Join  aB;  make  Jb  No.  2  equal  XX  Z, 
Fig.  3.  Join  bC,  which  gives  the  bevels  for  No.  2  wreath-piece. 
No.  1  wreath-piece  has  one  tangent  raking,  and  one  level,  hence 
there  will  be  but  one  bevel  required,  and  that  is  found  in  the 
angle  at  B,  Fig.  3.  No.  3  has  both  tangents  iucliuiug,  and  of 
different  inclinations,  hence  two  bevels  will  be  required. 

Make  Nd  No.  3,  equal  pv.  Fig.  3.  Join  dC:  make  Ve  No. 
8,  equal  r,  00,  Fig.  3.  Join  eD,  and  we  have  the  bevels  in  the 
angles  at  d  and  e  for  No.  3  wreath-piece.  No.  4  wreath-piece  has 
both  tangents  Inclining  the  same,  therefore  only  one  bevel  will  be 
required  for  both  joints. 

Make  W/No.  4,  equal  QfW,  Fig.  3.  Join  fE,  the  angle  at  i 
gives  the  bevel  for  No.  4  wreath-piece  at  both  joints. 

No.  5  wreath- piece  is  the  same  as  No.  3.  No.  6  wreath-piece 
has  one  tangent  inclining  and  the  other  horizontal,  and  as  they 
form  an  obtuee  angle,  two  bevels  will  bp  required. 

Make  xg^o.  6  equal  the  height  WG,  Fig.  3;  join  gf;  make 
yh  equal  ys.  Fig.  3;  join  hG  for  the  l)evels  in  the  angles  at  g 
and  h  for  No.  6  wreath-piece. 

For  the  increased  ■width  of  moulds  at  the  joints. 
Draw  parallel  with  tlie  tangents  the  half  width  of  rail  to  inter- 
sect hypothenuse  of  bevels;  as  for  No.  3  wreath-piece  at  j  aiul  1; 
for  No.  4  wreath-piece  at  m;  for  No.  6  wreath-piece  the  Hue  cuts 
at  n  and  p. 

Fig.  4.  Shows  the  face-mould  for  No.  1  wreathr^iece;  one 
tangent  U  incUning  and  the  other  horizontal  in  elevation,  and  as 
the  tangents  on  plan  form  a  light  angle,  only  one  bevel  is  re- 
quired, and  also  the  face-mould,  may  he  drau-n  icith  tin; 
trammel. 

Make  BH  equal  BH,  Fig.  3;  make  HA  scjuare  to  HB,  and 
equal  to  the  radius  OB  on  plan  Fig.  2;  draw  AO  and  BO  parallel 
with  HB  and  HA  for  the  rectilineal  parallelogram  OAHB  on 
the  cutting  plane. 

Proof.  The  chord  AB  and  diagonal  HO  must  equal  Bf  in 
elevation.  Fig.  3.  Make  A  2  and  A  3  each  equal  J"  IS,  Fig.  3; 
make  B  4  and  B  5  each  eciual  the  half  width  of  rail  (2'');  now 
pivot  the  trammel  at  O,  with  the  arms  on  the  major  axis  A O, 
and  trace  the  concave,  convex  and  falling  lines  of  face-mould. 

The  section  at  M  shows  the  bevel  found  in  the  angle  at  B,  Fig- 
3  applied  through  the  center  of  plank;  the  section  at  iV  shows  the 
try  square  is  applied,  and  the  block  pattern  shows  the  thickness 
and  width  to  saw  out  the  crook. 

Fig.  5.  Exhibits  the  face-nundd  fur  Xo.  2  wreath-piece;  as 
the  plan  is  the  segment  of  a  true  curve,  this  face-^nould  may  also 
be  draicn  with  a  trammel. 

Make  CJa  equal  CJa,,  Fig.  3.  With  C  as  a  center,  and  Cg, 
Fig.  3  for  a  radius,  draw  arc  at  B;  again,  with  J"  as  a  center,  and 
JB,  Fig.  3  for  a  radius,  draw  arc  inter^ecting  at  B,  connect  BJ; 
parallel  with  JB  and  JC,  draw  CP  and  BB  for  the  parallelo- 
gram JPBJC  on  cutting  plane. 

Proof.     The  diagonal  JB  must  equal  the  distance  bK,  Fig.  3. 

Connect  Ba  for  a  director;  parallel  with  Ba  draw  the  direc- 
tion of  minor  axis  PJ^  indefinite;  make  Pi^  equal  the  radius  BC, 
Fig.  2;  make  PG  and  F7  each  equal  the  half  width  of  rail  [2"  |. 
Let  C2  and  C3  each  ecjual  JlS,  Fig.  3,  and  B  4,  B  H  each  equal 
J  20,  Fig.  3;  pivot  the  trammel  at  P,  w  ith  the  arms  at  right 
angles  to  the  minor  axis  PF:  then  for  the  center  line  on  face- 
mould,  set  from  pencil  to  minor  pin  the  distance  BF,  now  place 


Plate  45.  20? 

the  pencil  in  the  point  at  J5,  and  the  minor  pin  in  the  major 
groove,  at  the  same  time  slide  the  major  pin  to  drop  into  the  minor 
groove,  fasten  the  major  pin  and  trace  tlie  center  line  on  mould. 

Proceed  in  the  same  manner  to  trace  the  concave  and  convex 
sides  of  mould. 

Make  joints  at  JB  and  Cat  right  angles  to  the  tangents  SJ" 
and  CJ.  The  section  at  A  shows  the  bevel  taken  from  the  angle 
at  h.  Fig.  2,  and  the  section  at  D  shows  the  bevel  taken  from  the 
angle  at  a,  Fig.  3.  They  are  applied  through  the  center  of  plank, 
and  the  shaded  parts  show  the  over  wood  to  be  removed. 

Fig.  6.  SJioivs  the  face-mould  for  No.  3  wreathrpiecc, 
which  is  termed  a  '■'■  utrcath-picce  with  an  intermediate  easing," 
or  accommodation  ivreath;  not  because  both  tnnijetits  are  in- 
clining, but  that  one  tangent  has  a  greater  inclination  tlian  the 
other. 

Make  DKd  equal  DKd.  Fig.  .3;  with  D  as  a  center  and  Dh, 
Fig.  3,  for  a  radius,  draw  arc  at  C;  again,  with  JK"  as  a  center  and 
.ZTC,  Fig.  3,  as  a  radius,  draw  arc  intersectim;  at  C;  connect  ICC; 
parallel  with  CK  and  DK  draw  DQ  and  CQ  for  the  parallelo- 
gram QCKD  on  the  cutting  plane. 

Proof.  The  diagonal  KQ  must  equal  the  distance  en.  Fig. 
3.  Join  Cd  for  the  director;  draw  the  chord  CD;  bisect  CD  at  2; 
bisect  2  Cand  2  Z)  at  3  and  4;  parallel  with  the  director  Cd  draw 
ordinates  indefinite  from  tlie  points  3,  2,  4,  and  D;  now  on  plan 
Fig.  2  bisect  the  chord  CD,  in  like  manner  at  the  points  3,  2,  4 
and  D;  make  K  XX  equal  Sd,  Fig.  3.  Join  C  XX  for  the 
director  on  plan;  parallel  witli  the  director  C  XX  draw  ordinates 
from  the  points  3,  2,  4  and  D  to  cut  tlie  concave,  center  and  con- 
vex side.s  of  rail  on  plan  at  5,  6  and  7.  Now  transfer  the  points 
2,  5,  6  and  7  from  the  ordinates  on  plan  Fig.  2  to  corresponding 
ordinates  on  face-nu.uld.  Fig.  0;  make  joints  at  Cand  D.  square 
to  the  tangents  CK  and  DK;  let  C8  aiul  C9  each  equal  dJ,  Fig. 
2.  Let  D  10  and  Z>  11  etiual  le.  Fig.  2.  Through  the  points 
trace  the  concave,  center  and  convex  sides  of  face-monld. 

The  section  A  sliows  the  bevel  found  at  e.  Fig.  2,  and  at 
.section  B,  the  bevel  found  in  the  angle  at  d,  Fig.  2.  The  bevels 
are  applied  from  tlie  upper  or  face  side  of  crook,  and  through  the 
center  of  plank;  observe  they  cross  the  tangents. 

Fig.  7.  Exhihlla  the  face-mouUl  for  No.  4  wreath  piece; 
the  tangents  both  have  the  same  iyiclitintion.  hence  only  one 
bevel  ivill  be  required  for  both  joints,  and  the  wreath-piece  is 
termed  a  v^reuth-piece  without  an  easing. 

Make  DL  equal  DL,  in  elevation.  Fig.  3.  With  Z)  as  a  cen- 
ter, and  the  distance  EJ,  for  a  radius,  draw  arc  at  E;  again,  witli 
Zf  as  a  center,  and  LD  for  a  radius,  draw  arc  intersecting  at  E; 
join  LE;  parallel  wiih  LE  and  LD,  draw  DR  and  ER,  for  the 
parallelogram  RDLE,  on  the  cutting  plane. 

Proof.  The  diagonal  LR  must  etiual  tlie  diagonal  LR,  on 
plan.  Fig.  2.  In  all  cases  when  the  two  tangents  have  the  same 
inciination  and  length,  the  diagonal  becomes  the  director. 

Make  tlie  joints  at  E  and  D  at  right  angles  to  the  tangeut-s 
LE  and  LD.  Draw  the  chord  DE;  also  ttie  diagonal  RL  bisects 
tlie  chord  at  .5.  Bisect  5  E  and  5  JD  at  6  and  7.  Parallel  with  the 
director  LR,  draw  ordinates  indefinite  from  the  points  Z),  7,  5,  6 
and  E;  draw  the  diagonal  RL,  on  plan,  Fig,  2,  bisects  the  chord 
DE  at  .5.  Bisect  5  E  and  5  jD  at  6  and  7.  Parallel  with  the 
director  LR,  draw  ordinates  to  cut  the  concave,  center  and  con- 
vex  ides  of  rail,  then  transfer  the  points  on  the  ordinates,  Fi^.  3, 


•:i08  Plate  45. 

to  correspoudiug  ordiuates  ou  the  face-uiould,  Fig.  7,  as  5,  8,  9,  10. 
For  the  increased  width  of  mould  at  the  joints,  make  E  3 
and  E  3  also  D  4  and  D  5,  each  equal  fm.  Fig.  3.  The  concave, 
center  and  convex  curves  of  face-mould  may  now  be  drawn 
through  the  points  indicated,  using  a  flexible  strip.  The  bevels 
for  both  joints  as  shown  at  sections  H  and  J,  are  found  in  the 
angle  at  /,  Fig.  3,  the  bevel  is  applied  so  as  to  cross  the  tangents; 
the  shaded  parts  show  the  width  at  the  joints  to  sav»'  out  the 
crooks.  At  the  narrow  part  of  mould  %''  of  overwood  may  be 
allowed  on  the  concave  side,  and  less  on  the  convex  side.  At 
that  part  of  the  mould  the  bevels  bleud,  and  the  side  of  rail  is  at 
right  angles  to  the  face  of  plank. 

Fig.  8.  Exhibits  the  face-moxiJd  for  No.  6  urcath-plccc;* 
one  tangent  GN,  is  horizontal,  and  the  other  NF,  is  inclining; 
tfie  ivreath- piece  is  termed  "a  wreath-piece  %vith  a  full  easing.^' 

Make  FN  equal  FN,  in  elevation.  Fig.  3.  With  JP  as  a 
center,  and  the  distance  Gni,  Fig.  S,  for  a  radius,  draw  arc  at 
G;  again,  with  iVas  a  center,  and  GN,  Fig.  3,  for  a  radius,  draw 
arc  intersecting  at  G;  join  NG;  let  it  be  observed  NG  I)ecomes 
the  director  for  the  ordinates.  Parallel  with  NG  and  NF,  draw 
FT  and  GT,  and  we  have  the  parallelogram  TGNF,  on  the 
cutting  plane. 

Proof.  The  diagonal  NT  must  iqual  the  distance  Gl  in 
elevation,  Fig.  3;  if  so,  the  angle  of  tangents  is  correct. 

Draw  the  chord  GF;  bise'ct  GF  at  18;  bisect  F  18  and  G 18 
at  30  and  19.  From  the  points  19,  18,  9.0  and  F,  draw  ordinates 
indefinite,  and  parallel  to  the  director  GN.  In  like  manner  on 
plan,  Fig.  3,  bisect  the  chord  in  IS,  19.  ;20  and  draw  the  ordinates 
parallel  with  the  director  GN  to  cut  the  concave,  center  and 
convex  curves  of  rail  on  plan,  as  shown  at  18,  31,  33  and  33. 
Now  transfer  points  from  plan  to  corresponding  lines  on  face- 
mould,  Fig.  7,  For  the  increased  width  of  mould  at  the  joints, 
make  F  3  and  F  3  each  equal  hp  ou  plan,  Fig.  3;  also  make 
G  4  and  G  5  each  equal  gn  on  plan,  Fig.  2,  then  trace  through 
the  points  for  the  concave,  center  and  convex  curves  of  mould, 
using  a  pliable  strip.  Add  on  two  or  more  inches  at  the  joint  G, 
to  help  the  easing  in  the  wreath-piece  to  connect  the  straight  rail. 

The  bevel  shown  at  section  L  is  tsiken  from  the  angle  at  g, 
P'ig.  8,  and  the  bevel  shown  at  section  F  is  taken  from  the  angle 
at  h.  Fig.  3.  Observe  they  do  not  cross  the  tangents,  as  there  is 
no  point  in  the  mould  that  is  equal  to  the  true  width  of  rail  [4"]. 
The  bevels  are  applied  from  the  upper  side  of  crook,  the  shaded 
parts  show  the  width  at  the  joints  to  saw  out  the  crook. 

Balusters.  If  it  be  required  to  find  the  length  and  location 
of  balusters  under  the  wreath  rail,  then  make  J" 34  No.  3  ou  plan, 
equal  Qa,  at  No.  3  in  elevation,  connect  34  B  for  the  director  of 
No.  3  wreath- piece  on  plan.  Fig.  3.  Also  make  E  2b,  No.  5 
wreath-piece  ou  plan  equal  Sd  in  elevation,  Fig.  3.  Connect 
S  25  for  the  director  of  No.  5  wreath-piece  on  plan.  The  small 
circles  indicate  the  location  of  balusters  on  plan. 

At  Nos.  1,  3,  3,  4,  .5  and  6  wreath-piece  on  plan  draw  from 
the  center  of  each  baluster  parallel  with  their  directors,  lines  to 
intersect  the  tangents;  the  black  dots  show  their  intersection  on 
the  tangents.  i^ 

Now  transfer  the  position  of  balusters  on  the  tangents  to 
their  respective  treads  in  elevation,  being  careful  to  space  them 

*  Note.— To  facilitate  reference  from  plan  to  cloviition,  and  also 
face-moulds,  numbers  are  used,  which  correspond  to  each  other. 


Pr.ATE  45.  9^: 

between  the  perpendicxilars,  as  thej-  are  shown  on  the  tangents 
on  plan.  The  small  circles  at  each  tread  show  their  location  in 
elevation.  From  the  center  of  each  baluster  draw  perpendiculars 
to  intersect  the  ruider  side  of  rail  as  shown.  The  height  of  scroll 
from  the  top  of  No.  1  step  to  tlie  imder  side  of  rail  we  will  say  is 
2''  Z",  and  the  elevation  Fig.  3  shows  No.  1  baluster  to  be  1" 
from  top  of  No.  1  step  to  the  under  side  of  rail.  Then  this  one 
inch  (\")  has  to  be  deducted  from  the  odd  balusters,  as  shown  in 
elevation;  thus,  the  second  baluster  measures  2 1^: '"' f rom  the  top 
of  step  to  underside  of  rail;  then  (2M^^— l''+"i' 3'^=2MJ^'0; 
No.  2  baluster  equals  2'  A:}i"  from  top  of  step  to  under  side  of 
rail.  The  third  baluster  on  No.  1  step  equals  5  J^^^;  then  5 K''' 
plus  V  Z"  and  minus  \"  equals  2'  'IM"  for  No.  3  baluster,  from 
the  top  of  No.  1  step  to  uuder  side  of  rail  when  in  position. 

The  balusters  on  No,  4,  7,  8,  13,  treads,  and  the  first  baluster 
on  the  landing  No.  17,  are  the  same  length  as  the  first  baluster; 
those  on  No.  3,  0,  9,  12  and  14  treads  are  "^A"  longer  than  the 
first;  the  balusters  on  No.  10  and  11  treads  are  %''  longer;  on 
No.  5  tread  a  M"  longer;  on  No.  2  tread  2>.<^^  longer;  on  No.  15 
tread  V  longer;  on  No.  16  tread  4^''  longer,  and  the  second  bal- 
uster at  the  landing  No.  17  equals  IM^^  longer  than  the  first 
baluster;  the  balusters  on  the  level  will  be  Z"  longer  than  the 
first.  The  balusters  under  a  wreath  having  an  easing,  may  vary 
a  trifle,  but  this  system  will  be  correct  enough  for  all  practical 
purposes. 

If  desired,  the  exact  location  of  each  haluster  may  bo  found 
on  the  face-mould  and  transferred  to  the  wreath-piece  in  the 
rouKli.  When  the  mould  is  shifted  on  the  tangents  to  its  exact 
position  on  the  croolc,  tlien  tlie  center  of  eacli  baluster  may  lie 
pricked  through,  and  also  the  direction  of  eacli  ordinate,  then 
bored  for  the  balusters  to  a  templa,te  made  to  the  pitch. 

To  do  this,  extend  the  center  of  balusters  to  intersect  the  tan- 
gents as  shown  in  elevation.  Fig.  .3,  for  No.  4  wreath-piece:  now 
transfer  from  tlie  tangents  in  elevation  to  face-mould.  Fig.  7,  as 
shown  by  the  dots;  then  parallel  witli  the  director,  draw  lines  to 
intersert  the  center  or  falling  line  of  mould,  tlius  establishing-  tlieir 
location. 

To  find  the  pitch  to  cut  the  template  for  the  wreath-piece. 
Fig,  6,  make  E,  PP,  No.  5  in  elevation.  Fig.  3,  equal  the  shortest 
distance  from  D  to  tlie  director  C,  XX  No.  3  on  plan.  Fig.  2;  draw 
RR,  PP,  Fig.  3  for  the  anales  at  RR  or  PP,  which  gives  the 
cut  for  the  template  PP,  E,  RR,  to  guide  the  bit  when  boring. 
For  No.  7  mould  the  template  is  made  to  tlie  pitch  TEJ  No.  4 
in  elevation,  Fig.  3.  For  Fig.  8  mould  the  template  is  made  to 
the  pitch  XgF  No.  6  on  plan.  Fig.  3,  and  held  at  right  angles  to  the 
ordinates,  as  ab,  Fig.  7,  or  6  a.  Fig.  6,  r 

As  tlie  face-mould  is  drawn  the  upper  or  back  of  rail  is  shown. 
The  opposite  side  will  be  the  underside  or  lircnat  of  rail.  The  boring  of  a 
rail  for  balusters  is  easily  done,  iind  the  ijcst  results  will  be  obtained  by 
doing  the  boring  on  the  stairs  after  the  rail  is  hung  and  in  Its  proper 
place.  If  the  balusters  be  square  at  the  top,  then  each  baluster  is 
plumbed  to  place  and  filled  in  between. 

The  lower  end  of  scroll,  containing  the  eye,  may  be  worked  from 
a  tliick  piece  of  plank  by  marking  out  the  plank  to  the  pattern  No.  1 
on  plan  Fig.  2,  and  sawing  out  the  same  neat  and  square  from  the 
face  of  plank,  and  making  the  joint  to  the  bevel  shown  by  the  dotted 
lines  at  No.  1  in  elevation,  I<'ig.  3;  thus  avoiding  the  face-mould  No.  1, 
Fig.  4,  and  also  the  joint  at  A,  on  plan  Fig.  2.  In  tliis  case  the  twist 
line  must  lie  carried  around  so  as  to  give  a  graceful  curve.  The  re- 
ciprocal scroll  shown  at  Fig.  5,  Plate  G,  may  be  applied  here  with 
pleasing  ett'ect. 


210  Pi.ATK  46. 

PLATE  46. 

Plate  46.    Exhibits  14  profiles  of  hand-rails  one-half  full 

size. 

Figs.  3  and  4  show  the  "pew  back"  pattern;  Fig.  8  suits 
well  for  an  altar  or  office  rail;  Fig,  9  for  capping;  Fig.  11  for  cap- 
ping on  iron;  Fig.  13  suits  well  for  a  wall  rail.  For  square  top 
balusters,  the  underside  or  "l)reast"  of  rail  should  be  rebated 
out,  as  at  A  and  S,  Figs.  3  and  6;  then  filled  in  between.  Fig. 
5  shows  the  straight  rail  made  in  two  pieces.  These  rails  are 
classed  as  '-double  rails,"  with  the  exception  of  Nos.  9  and  11. 

Straight  Rail,.  If  the  material  is  dry,  the  straight  rail  may  be 
made  from  plank  as  the  cheapest  way ;  11  very  large  double  rails,  then 
use  inch  stuff  glued  to  a  pine  core,  as  shown  at  x'ig.  3,  or  in  several 
thicknesses,  as  shown  at  Figs.  2  and  7. 

"When  ripping  out  the  straight  rail  select  plank  that  have  squared 
edges  and  thoroughly  dry.  Tlien  they  will  not  spring  much,  if  any. 
If  the  plank  be  springey,  then  rip  up  the  center  and  joint  off  straight. 
If  the  rail  be  bowed  up  or  down,  it  will  be  easy  to  straighten  on  the 
stairs  when  putting  in  the  balusters,  but  if  crooked  sideways,  it  is 
more  difficult  to  straighten,  but  it  can  be  done  by  bracing  the  rail  a 
little  over  straight  the  other  way,  and  allowing  tbe  braces  to  remain 
over  night  after  the  balusters  have  all  been  well  glued  to  place;  then 
when  the  braces  are  removed  the  rail  will  come  about  straight.  To 
do  this  requires  one  to  have  some  experience  in  hanging  rails.  By 
thoroughly  wetting  the  concave  side  of  the  crooked  part,  then  forc- 
ing it  out  of  straight  the  other  way  and  leaving  until  dry,  the  rail 
will  be  about  straight.  Short  kinks  in  the  straight  rail  will  some- 
times occur  in  this  way:  the  material  being  cross-grained,  or  a  knot 
curl  on  the  side  of  rail,  will  cause  short  kinks,  particularly  if  the 
stuff  be  not  thoroughly  dry.  When  rails  are  worked  out  for  some 
time  before  they  are  required  these  defects  should  be  avoided  much 
as  possible,  for  a  rail  may  be  worked  out  nice  and  straight,  then 
placed  on  the  rack  until  v.'anted,  and  upon  examination  will  be  found 
crooked.  This  is  a  difficulty  the  stair-builder  labors  under,  and 
hence  the  necessity  that  the  material  for  straight  rail  should  be  made 
from  the  best  lumber,  straight  in  grain  and  thoroughly  dry. 

Black  walnut  requires  one  year  for  every  inch  in  thickness  to  dry, 
and  then  it  must  be  well  "stuck"  on  strips  up  from  the  ground,  where 
the  air  can  circulate  freely  around  the  pile.  Owing  to  being  a  dark  wood 
It  does  not  dry  out  so  soon  as  any  of  the  light-colored  woods,  and  if 
near  the  ground  will  never  dry.  It  is  the  best  native  wood  we  have 
to-day  for  hand-rails,  balusters  and  newels;  the  sap  part  is  objec- 
tionable, and  should  not  be  used  in  first-class  work,  but  in  second- 
class  work  may  be  stained*  to  imitate  the  heart  wood.  The  sap  in 
ash  wood  is  like  the  heart  wood,  and  tlierefore  may  be  used.  The  sap 
part  of  oak  should  be  avoided,  as  it  is  mostly  damaged  by  the  worm, 
and  in  cherry  the  sap  .should  be  cut  away,  as  it  is  very  inferior  to  the 
heai't  wood. 

The  Wreath  Part.  For  double  rails  the  wreath-piece  should  be 
made  in  one  piece  from  well  sea.soned  lumber,  as  it  is  very  tedious 
work  to  make  the  Avreath  part  of  double  rails  in  two  or  more  pieces 
when  fitting  them  together.  It  may  )>e  difficult  to  find  plank  thick 
enough  for  large  double  rails.  In  that  case  the  thickness  may  be  in- 
creased by  gluing  the  required  amount  to  the  underside  of  crook. 
This,  however,  sliould  never  be  done,  if  possible,  a.s  the  glued  joints 
work  out  to  a  feather  edge,  and,  if  exposed  to  dampness,  may  ruin 
the  wreath;  plank  thick  enough  for  the  wreath  rail  should  in  all  cases 
be  used  for  flr.st-class  work. 


PLATE  47. 


Plate  47.  Shf>ws  the  construction  of  an  open  newel  stair' 
case  having  a  qxiailmmjular  well'-hole  and  close  front  strimj, 
pnishcd  irith  string  mouidings  and  rosettes. 

^- To  color  the  sap  of  hlack  wahmt.  Take  one-half  gallon  of  water, 
one-half  pound  of  dry  burnt  umber,  one-quarter  pound  of  rose  pink, 
one-quarter  pound  of  Vandyke  brown;  mix  thoroughly,  apply  with 
a  sponge,  allow  to  dry  and  rub  off;  when  oiled  will  be  uniform  with 


Plate  47.  211 

Pig.  1.  [Scale  H^^=l  footj.  Shows  the  plan  having  18 
risers.    The  main  newel  is  S'^yiS'^,  and  the  minor  newels  are 

This  style  of  a  stair-case  belongs  to  the  dog-leg  type,  having 
newels  in  the  angles,  and  the  rails  to  butt  the  newels,  either 
straight  or  with  the  old  style  "ramp  and  knee"  or  "goose  neck  ; 
sometimes  the  minor  newels  are  allowed  to  extend  up  and  finish  with 
turned  finals,  at  other  times  the  rail  is  mitered  around  the  newel, 
forming  a  cap  with  turned  top,  and  the  lower  end  of  newel  ex- 
tends down  below  the  ceiling,  far  enough  to  receive  the  lower 
edge  of  string  and  finish  with  a  drop. 

Eig.  2.  [Scale  %''=\  foot].  Shoxos  the  plan  of  the 
minor  newel  at  Nos.  8  and  9  rise. 

The  face  of  risers  is  located  at  the  center  of  newels;  A  and 
B  show  the  front  string  housed  into  the  posts  half  an  inch;  the 
dotted  lines  show  the  steps  housed  into  the  posts  and  string  M^'. 

Fig.  3.  SJwws  the  elevation  of  four  sides  A,  B,  C,  D, 
of  post,  Fig.  2,  and  also  the  strings  connecting  the  same. 

*  The  treads,  risers  and  strings  are  housed  into  the  newels,  and 
the  string  mouldings  are  allowed  to  butt  against  the  posts.  The 
post  is  mortised  to  receive  the  rail,  which  should  be  tenoned  and 
bolted  at  the  joint.  -' 

If  hard  wood  finish,  the  strings  may  be  veneered  on  a  pine 
core.  H  shows  the  core,  and  K  the  veneer  ^'^  thick,  which  is 
glued  and  well  clamped  to  the  pine  core.  J  shows  the  shoe 
grooved  out  on  the  underside  to  straddle  the  string,  and  on  the 
upperside  to  receive  the  balusters.  L  shows  the  filler  cut  in 
between  the  balusters.  N  shows  the  plaster,  and  P  a  moulded 
strip  to  cover  the  joint  of  plaster.  R  shows  the  carriage.  S,  the 
joist  at  the  platform  and  lauding. 

The  posts  and  strings  may  be  chamfered,  paneled  and 
moulded  in  a  variety  of  ways  to  suit  the  style  and  taste  of  the 
architect  and  stair-builder.  The  post  at  Nos.  12  and  13  rise  is 
lined  off  similar  to  Figs.  2  and  3. 

Fig.  4.  Shows  the  plan  of  post  at  the  landing  No.  18  rise 
Tlie  face  of  rise  being  at  the  center  of  post. 

Fig.  5.  Sfioias  the  elevation  of  post  and  the  raking  and 
level  strings  connecting  the  same. 

C,  D,  E,  F,  shows  the  sides  of  post  lined  off  to  correspond 
•with  plan,  Fig.  4.  The  rail  T  extends  to  the  post  straight.  V 
shows  the  floor.  V,  the  rough  flooring,  X  shows  the  stripping 
underneath  the  joist  for  lathing.     N  indicates  the  plastering. 

The  rail  is  set  V  %"  from  the  floor  to  the  top  on  the  level, 
and  on  the  rake  2'  ^"  from  the  top  of  step  to  the  upper  side  of 
rail,  plumb  over  the  face  of  rise.  c- 

Fig.  6.  Shows  a  method  of  tnakiiuj  and  gluing  up  box  or 
b%iilt  posts. 

C and  E  are  the  two  narrow,  and  D  and  Pare  the  two  wide 
pieces;  J"  and  J"  show  the  piue  core.  The  sides  C,  D,  E  and  F 
should  be  made  from  two  inch  stuff,  and  of  perfectly  dry  material. 
A  jointer,  to  joint  and  take  the  sides  out  of  wind,  and  a  pony 
planer  to  size  them  to  an  even  thickness,  are  the  best  tools  for 
preparing  the  material  for  box  or  pedestal  posts.  The  pine  core 
J  J  is  made  to  the  proper  width  and  glued  to  the  wide  sides  D  and 
F,  first,  then  let  dry,  afterwards  glue  the  internal  angles  and  the 
edges  of  the  narrow  pieces,  put  a  clamp  at  each  end  and  one  at 
the  center,  so  as  to  draw  up  the  naiTOW  pieces  close  to  the  pine 
core;  then  put  all  the  clamps  on  the  wide  pieces  D  and  F  that 
will  be  thought  necessary  to  make  the  joints  close. 


31^  Tlate  4S. 


Carpentry  and  Joinery, 


Carpentry.  Is  properlj'  divided  into  tliree  branches,  con- 
stnictivc,  descripthic  and  mcchaniad. 

Constructive  Carpentry.  Is  divided  into  '-carpentry 
and  joinery."  tlie  distinguishing  featnre  being  less  tools  required 
tor  the  carpent(U'  proper,  who  takes  charge  and  erects  the  naked 
carcase  of  the  building.  Then  afterwards  the  joiner  prepares 
the  doors,  sash,  shutters,  stairs  and  other  finish  for  and  com- 
pletes the  structure.  In  our  country  the  diit'ereiiee,  however,  is 
very  artificial,  as  most  carpenters  have  all  the  tools  reqiured  in 
the  art  of  joinery,  with  the  exception  of  the  stairs.  In  large 
cities  that  branch  of  joinery  is  made  a  separate  business. 

Constructive  Carpentry  shows  the  practice  of  shaping  and 
jointing  the  different  pieces  of  wood  in  the  erection  and  com- 
pletion of  a  building,  according  to  the  design  and  intention  of  the 
architect. 

Descriptive  Carpentry.  Shows  the  lines  or  methods 
for  forming  various  kinds  of  work  on  plan,  elevation  and  detail, 
acccmling  to  and  by  the  rules  of  geometry. 

Mechanical  Carpentry.  Shows  how  to  arrange  the  dif- 
ferent timl)ers  of  a  building  relative  to  their  strength,  and  the 
strain  to  which  they  may  lie  subjected.  This  brancli  of  carpen- 
try is  becoming  inore  studied  by  the  young  carpenter  who  asjiires 
to  the  upper  rung  in  the  ladder  of  that  noble  and  honored  occu- 
pation. The  best  and  most  practical  books  for  the  young 
American  to  study  in  this  branch  of  carpentry  is  the  "American 
House  Carpent(!r,"  and  also  "Transverse.  Strains,"  by  Mr.  H.  G, 
Hatfield.  In  this  branch  of  cariientry  we  will  give  a  fev\'  rules 
to  calcidate  the  strength  of  timber,  aiul  recomnienil  the  student 
to  the  dilTerent  works  herein  rel'evred  to  lor  a  more  extensive 
elucidation  vii  the  subject. 


PLATE  48. 


Plate  48.  ExhihUs  the  construction  of  the  ''Hip,^'  "Faf- 
Inf  (tnd  ''JdcJi"  Rafters  for  a  roof  having  the  angles  on  q)l(in, 
aJL  right  angles. 

"Fig.  1.  [Scale  }4^^=1  foot].  Shows  two  right  angles  of  a 
lmildi)tg  to  he  hipcd. 

t  KG,  GA  and  AL  indicate  the  outside  line  of  walls;  ZZ, 
the  inside  of  walls.  Bisect  GA  at  N;  make  GK  and  AL,  each 
equal  AN;  draw  KL  parallel  to  GA:  at  right  angles  to  GA, 
draw  a  line  from  N  to  intersect  KL  at  H;  draw  GH  and  AH 
for  the  seat  of  the  center  line  of  hip.  Now  space  off  for  the 
seat  of  jack  rafters.  B,  B,  &c. 


Plate  4S.  211 

Pigi  2.    Shoios  the  elevation  of  "common  rafters.'^ 

GA  is  the  width  of  building  (12''  C''),  and  agrees  with  GA. 
Fig.  1.  JCX  shows  the  walls,  yy,  the  ceiling  joist  resting  ou 
the  "wall  plates"  W;  bb  indicates  the  "raising  plate"  flush 
with  the  walls  on  the  outside. 

Bisect  GA  nth;  draw  hD  perpendicular  to  AG;  make  tlie 
height  from  top  of  raising  plate  at  J  to  D,  to  equal  one-third  the 
span  GA  {i^  0'^),  which  is  termed  a  "third  pitch."  Draw  DG 
and  DA  to  the  top  edge  of  raising  plate  bb,  for  the  length  of 
common  rafter  from  the  "toe"  to  the  center  of  "ridge  plate"  at 
F;  allow  the  half  thickness  of  ridge  plate  less,  when  cutting  the 
rafter. 

Now  return  to  Fig.  1.  Draw  HE  at  right  angles  toHG,  and 
equal  to  hD,  Fig.  2.  Draw  EG  from  the  top  edge  of  raising 
plate  b  to  the  center  of  ridge  plate  at  F,  for  the  length  of  hip. 
When  cutting  the  hip  to  the  proper  length,  deduct  the  half  thick- 
ness of  ridge  plate,  which  is  equal  to  Ed  on  the  inclination  of  hip 
as  shown,  carried  up  from  the  intersection  of  the  seat  of  hip  with 
the  scat  of  ridge  plate  at  H. 

To  find  the  length  of  jack  rafters.  Make  HJ,  Fig.  i 
equal  DA,  Fig.  2,  the  length  of  common  rafter  from  the  toe  to  the 
center  of  ridge  plate.  From  J,  draw  a  line  parallel  to  LA,  inter- 
secting GA  prolonged;  at  S,  draw  SH  \or  the  center  line  of  hip, 
set  off  the  half  thickness  of  hip  parallel  to  SH, 

Proof.  SH  must  equal  the  length  of  hip  GE;  CH  is  the 
same  length;  now  extend  the  jacks  from  L  to  J  shown  by  the 
dotted  lines.  Then  JS,  2  3,  <tc.,  are  the  lengths  of  the  jack 
rafters,  and  SH  or  CH  is  the  length  of  the  hip.  Now,  if  the  de- 
velopment HJS  were  elevated  into  position,  it  would  coincide 
with  HLA  on  plan. 

Bevels.  The  bevel  in  the  angle  at  D  gives  the  down  cut 
for  both  the  common  and  jack  rafters;  the  bevel  at  G  gives  the 
cut  for  the  "foot"  of  both  common  and  jack  rafters.  The  bevel 
in  the  angle  at  M  gives  the  down  cut  at  the  upper  end  of  liip 
rafter,  and  the  bevel  shown  in  the  angle  at  J"  gives  the  cut  for  the 
foot  of  hip  rafter.  The  angle  at  D  gives  tiie  bevel  for  the  upper 
end  of  hip  against  the  ridge  plate,  if  applied  on  the  plane  of  back- 
ing from  the  side  which  is  done  after  the  hip  is  backed;  the  angle 
at  Tgives  the  .side  cut  of  jack  rafter  against  the  hip. 

To  "back"  the  hip  so  as  to  range  with  (he  jack  rafters;  any- 
whcnion  the  seat  of  hip  GH,  say  at  O,  draw  a  line  at  right  angles 
to  GH,  intersecting  GilTaiid  GN  at  P  and  Q;  from  the  center 
O,  draw  an  arc  to  tangent  the  inclination  GE  of  hip,  and  inter- 
sect the  seat  of  hip  GH  ni  R,  join  RP  and  RQ,  and  the  angle 
at  R  gives  the  bevel  to  back  the  hip;  a  section  of  liip  is  shown  at 
R.  *    A  more  practical  method  is  shown  at  next  plate. 

At  C  in  elevation,  Fig.  2,  is  shown  the  position  of  "Purlin" 
having  th(;planeof  its  vertical  sides  perpendiculartoi)lan.  Tolind 
the  cuts  for  a  purlin  against  the  hip,  in  a  case  of  this  kind  there  is 
no  difliculty;  if  the  plane  of  the  sides  of  hip  be  pluml>,  and  the 
purlin  be  parallel  with  the  walls,  then  the  down  cut  on  purlin 
will  be  a  right  angle  to  the  upper  edge,  and  the  side  cut  against 
the  hip  will  be  equal  to  the  angle  that  the  seat  of  purlin  makes 
with  the  seat  of  hip  on  plan.  In  this  case  the  bevel  shown  in  the 
angle  at  U,  Fig.  1,  gives  the  side  cut. 

"■  *This  method  of  flndins  the  b:if:KiiiK  for  the  hip  rafter  is  ascribed 
to  William  Pope  l)y  Godfrey  Eii'lsards,  in  his  translation  of  the 
First  Book  of  Andre-w  Pulladio,  187'o.— Stuart's  Dictionary  of  Arch, 


214  Plate  48.  - 

At  B  is  shown  another  position  for  the  purlin,  the  sides 
being  oblique  to  plan,  or  perpeudicular  to  the  inclination  of  the 
common  rafter.  The  method  to  find  the  cuts  for  a  purlin  in  this 
position  is  shown  at  Figs.  3,  4  and  5.     [Scale  >2''^=  1  foot.] 

Fig.  3.    Shows  a  section  of  purlin  ^"  by  9". 

Apply  the  bevel  shown  at  2),  Fig.  2,  from  the  upper  side  of 
purlin,  and  draw  the  plumb  line  AC  across  the  section;  at  right 
angles  to  AC  draw  .£72  and  D  .3. 

Fig.  4.     Shoivs  how  to  find  the  doivn  cut  against  the  hip. 

Let  AB  indicate  the  "arris"  of  purlin  shown  at  E,  Fig.  3; 
parallel  with  AB  draw  the  depth  of  purlin  at  C(9'^);  set  a  gauge 
to  equal  D  3,  Fig.  3.  The  dotted  line  DE  indicates  tlie  gauge 
line  drawn  parallel  to  AB\  now  set  a  bevel  to  the  angle  that  the 
purlin  makes  with  the  hip  on  ))lan,  which  in  this  case,  the  hip 
being  square,  the  bevel  will  be  an  angle  of  4.5  degrees,  and  is 
shown  in  the  angle  at  U,  Fig.  1. 

Then  apply  the  bevel  found  in  the  angle  at  U,  Fig.  1,  from 
the  arris  AB  as  FG,  intersecting  DE  at  2;  from  2,  and  at  right 
angles  to  AB,  draw  3  3;  join  F'S  for  the  bevel  in  the  angle  at 
AF  o,  required  for  the  down  cut. 

Fig.  5.  Sliows  how  to  find  the  side  cut  of  inirlin  against 
the  hip  rafter. 

Let  AB  iudicate  tlie  arris  E,  Fig.  3.  Make  BC  e(3ual  t\w 
breadth  AE,  Fig.  3  [5^^J.  Let  BJE7  equal  E  2,  Fig.  3.  Draw  tlie 
gauge  line  BE  parallel  to  AB;  from  the  arris  AB,  apply  the 
bevel  found  in  the  angle  at  U,  Fig.  1,  cutting  the  gauge  line  DE 
at  3.  At  right  angles  to  AB,  draw  3  4.  Join  Hi  for  the  bevel 
required  in  the  angle  AH4. 

This  method  of  finding  the  bevels  for  the  cut  of  purlin 
hutting  the  hip,  is  practical,  as  they  may  be  lined  otf  on  the  tim- 
ber, when  the  material  is  on  the  "trestles."  * 

Fig.  6.  Exhibits  the  rear  and  part  of  a  main  biiUdiiig 
on  ))lan. 

AE,  FC  and  BD  indicate  the  line  of  walls.  Tin;  interna' 
angle  at  J*  must  have  a  valley  to  form  a  junction  with  the  rear 
wing;  also  the  plane  of  that  part  of  roof  between  the  hip  and 
valley  will  intersect  with  the  plane  of  roof  on  the  opposite  side 
forming  a  short  hip.  The  width  AB,  of  main  building  is  32'  0", 
and  the  wing  CD,  20^  0''. 

How  to  lind  the  length  and  cuts  of  hip  and  valley  rafters, 
also  the  length  and  cut  of  jack  rafters  between  the  hip  and  valley 
rafter. 

Bisect -E7G  at  H.  draw  a  line  from  JTindelinite  and  i)aralli'l  io 
AE;  imi\<{^  HL  ^'<[Ui\\  HE,  connect  JE7Z/ for  the  seat  of  long  hip  on 
•'♦■nter  line;  join  LG  tor  the  seat  of  short  hii>  on  the  center  line; 
<lrHw  CD  at  right  angles  to  DB;  bisect  CD  at  M:  di'aw  MN 
indefinite,  intersecting  EG  at  P,  also  interseethig  LG  at  Q; 
join  QF  for  the  seat  of  vallev  rafter  on  its  center  line.  I'rolong 
the  slioH,  hip  LQ  to  intersect  the  common  rafter  at  R,  or  the  hi)) 
may  lie  continued  to  G,  and  the  conunon  rafters  cut  b)  butt  the 
hi)i  from  R  to  G.  Now  set  otf  on  each  side  of  the  center  line 
of  hips  and  valley  the  halt  thickness  of  hip  and  ^•alley  rafters; 

*This  system  of  lievels  for  the  cut  of  purlins  against  the  hip  Avas 
first  published  Iiy  Mr.  Peteu  Nicholson,  in  1793.  The  system  is  shown 
more  at  lar;re  on  Plate  .50,  where  the  student  is  referred  for  a  moJ'J 
compreheusiv  e  study  of  the  priuciplo. 


Plate  48.  215 

draw  the  jack  rafters  2  3,  2  3,  &c.,  to  suit  the  space  as  shown. 
This  completes  the  plan  for  the  two  hips  EL  and  LQ,  also  the 
valley  QF  &ud  jack  rafters  2  3,  &c.,  as  required  for  the  plan. 

Fig.  7.  Slioios  the  elevation  of  common  and  hip  rafters 
far  the  main  building. 

Draw  AJB  parallel  to  EG,  intersecting  HJ  at  K;  make  KJ 
equal  half  the  span  AB,  or  16'  0",  for  the  pitch  of  roof,  which 
is  termed  a  "half  pitch";  join  JA  and  JB  for  the  length  of  com- 
mon rafter.  Prolong  KA  equal  to  the  seat  EL  of  hip  on  plan, 
Fig.  6,  as  KS;  join  JS  for  the  length  of  hip. 

Fig.  8.  Shows  the  elevation  and  length  of  the  common 
rafter  for  the  rear  hidlding,  and  also  the  length  of  valley  rafter 
connecting  the  warn  buildinc/. 

■  Make  MT  at  right  angles  to  CD  and  equal  to  CM,  for  a 
half  pitch.  Join  TC  aud  TD  for  the  length  of  common  rafter. 
Prolong  MC  to  U  equal  to  FQ,  on  plan,  for  the  seat  of  valley 
rafter.     Join  TU  for  the  length  of  valley  rafter. 

Now  return  to  plan,  Fig.  6.  Make  FV  equal  TC  Fig,  8, 
also  make  HW  equal  AJ,  Fig,  7.  Join  EW  aud  VF,  also 
connect  VW  for  the  center  lines  of  hips  and  valley  rafters. 
Then  when  the  trapezoid  EWVF  is  elevated  into  position, 
it  will  agree  with  the  trapezoid  ELQF,  on  plan. 

Proof.  The  center  line  EW  of  hip,  must  agree  with  the 
length  of  hip  JS,  in  elevation.  Fig.  7;  also  the  center  line  FV, 
of  valley  rafter,  must  agree  with  the  length  TU,  in  elevation, 
Fig.  8. 

Now  after  the  hip  is  backed,  set  oif  on  each  side  of  the  cen- 
ter line  of  hips  and  valley,  the  half  thickness  of  timber  measured 
on  the  plane  of  backing.  Then  extend  the  jacks  to  intersect  the 
hips  aud  valley  rafters  as  2  4  and  5  4,  &c.,  for  their  different 
lengths.  If  at  the  point  R,  a  line  be  drawn  parallel  to  FN, 
cutting  WV  prolonged  at  X,  then  WX  will  be  the  length  of 
short  hip  at  the  center,  to  butt  the  common  rafter  at  i?,  when  in 
position.     Draw  the  joint  at  X  at  right  angles  to  RX. 

The  bevel  in  the  angle  at  Y  gives  the  side  cut  against 
the  common  ratter,  if  the  bevel  be  carefully  applied  from  the 
outer  edge  VW  after  the  hip  has  been  backed.  The  down  cut  is 
shown  at  T,  Fig.  8,  aud  is  applied  to  all  hips  and  valley  rafters. 
The  bevel  shown  at  6,  Fig.  8,  applies  to  the  foot  of  all  hips  and 
valleys.  The  bevel  in  the  angle  at  Z  gives  the  side  cut  for  the 
jacks  against  the  hii>s  and  valley  rafters.  The  down  cut  for  all 
jack  and  common  rafters  are  alike,  and  the  bevel  is  shown  at  O, 
Fig,  7.  The  bevel  for  the  foot  of  all  common  and  jack  rafters 
that  rest  on  the  raising  plate  is  shown  at  X,  Fig.  7. 

The  bevel  at  Z  will  give  the  cut  of  hip  against  the  ridge  plate 
at  W,  but  must  be  applied  from  the  inner  side  4  4  after  tiie  hip 
is  backed.  The  valley  rafter  will  need  no  backing,  the  edge  being 
left  square  in  this  case.  If  exposed  aud  the  sheathing  to  form 
a  finish,  then  the  top  edge  of  rafter  must  be  worked  into  a  V 
shape,  the  bevel  being  the  same  as  for  the  backing  of  the  hip. 

As  the  valley  rafter  forms  a  right  angle  with  the  hip  at  Q  on 
the  plan,  then  the  cut  against  the  hip  rafter  WFwill  be  a  square 
rut,  if  applied  before  any  backing  is  done  to  the  valley  rafter;  7,  7, 
shows  the  raisiug  plate;  the  "foot"  of  rafter  is  notched  out,  form- 
ing a  "heel"  to  butt  the  raising  plate  and  ueutralize  the  tlirust  of 
ratter. 


216  Tlate  49. 

Fig.  9.  Slioivs  a  ffraphicnl  method  to  determine  the  stiffest 
beam  that  can  be  cut  frorii  round  timber. 

ii't  AB  indicate  the  diameter  of  a  round  losj;  bisect  AS  at 
C;  with  A  and  B  as  centers,  draw  arcs  from  Cto  interstct  the 
circumference  of  loj^  at  E  and  D\  join  AE,  EB.  BD  and  AD, 
forming  the  rectiliutal  parallelogram  AEBD  lor  the  size  of 
beam. 


PLATE  49, 

Plate  49.  Shoivs  an  cc-fiy  latthod  lyw  to  find  the  lewjth  of 
/(//>  ((nd  Jar);  rafters,  and  cuts  for  the  same,  when  the  angles  of 
bu'ddbiij  are  obtuse  or  acute. 

Fig.  1.     [Scale  M"=l  foot].     Shows  the  plan. 

AB,  jBCand  CD  sliow  tlie  outside  line  of  walls:  ZZ  sliovvs 
the  inside  line  of  waiis;  vy,  &c.,  indicate  the  line  of  raising  plate, 
wliich  lias  to  be  well  nailed  to  the  joist  to  resist  the  thrust  of 
rafters;  XX  show  the  "lookout  joist"  for  cornice. 

Bisect  AD  at  G,  draw  GH  iiarallel  to  AB  for  the  center  of 
ridge  plate;  bisect  the  angle  ABC,  also  the  angle  BCD,  at  E 
and  F;  draw  BE,  also  CF  prolonged,  to  intersect  GH  at  K; 
then  ifB  and  iiCC  are  the  seat  lines  for  the  center  of  hips.  On 
each  side  of  GH,  set  off  the  half  thickness  of  ridge  plate,  also  set 
olf  the  half  tliickness  of  hips  on  eacli  side  of  the  seat  lines  BK 
and  CK.  Now  space  off  2,  U,  V,  W,  &c.,  for  the  seat  of  com- 
mon and  jack  rafters,  and  draw  US,  Q  4,  R  5,  M 6,  &c.,  at 
riglit  angles  to  the  line  of  walls,  to  intersect  the  seat  of  hips  at 
P.,  3,  4,  4,  5,  5  and  6,  6;  in  this  case  the  rafters  occupy  position 
directly  over  the  joist. 

Fig.  2.  E.vliihiis  the  Icwjih  of  common  and  jack  raff  cm, 
■in  elevation,  the  Icnrjth  of  each  jacli  is  <jiven  on  the  common  rafter. 

Draw  XyfoT  the  span  [vy  0"j;  bisect  Xj  at  W,  draw  the 
iicig'it  Wy  at  right  angles  to  X.F  and  equal  to  XW c'  0^',  plus 
tl:e  tliickness  of  raising  plate  [l"J  equals  C  1".  Draw  the  incli- 
nat.on  of  rafter  from  tlie  center  of  ridge  plate  at  V,  to  the  edge 
of  raising  plate  at  X  and  ITfor  the  lenglii  of  common  rafters,  less 
the  half  thickness  of  ridge  plate. 

Now  from  the  intersection  of  the;  seat  of  jack  rafters,  witli 
the  seat  of  hip  at  3,  3,  &c.,  on  plan  Fig.  1,  draw  lines  parallel  to 
AB,  Fig.  1,  !o  intersect  the  common  ratter  in  elevation,  Fig.  2, 
at  the  points  J,  H,  G,  F,  E,  D,  C,  B,  A,  then  XJ  is  the  s^hort- 
est.  and  XA  is  next  to  the  longest  jack  rafter.  On  the  opposite 
si'de  ot  hip,  the  jacks  co? respond  in  Icngtli. 

On  lfi8  short  hip,  CK  for  the  obtuse  angle,  the  length  of 
jacks  an;  found  in  the  same  manner.  In  elevation.  Fig.  2,  yK 
shows  the  Icnirth  of  jack  rafter  correspoiidintc  1o  MG,  Fig.  1. 

Make  WX" equal  BK.  Fig.  1.  Draw  VK  to  the  upper  arris 
of  raising  plate,  as  shown  for  the  inclination  and  length  of  tii(! 
long  hip,  to  the  center  of  ridge  plate.  Make  WS  equal  KC, 
Fig,  1.  Draw  VS  to  the  edge  of  raising  plate,  as  shown  for  the 
lengtli  of  short  hip  to  the  center  of  ridge  plate.  When  cutting 
the  rafters,  the  half  thickness  of  ridge  plate  must  be  deducted. 

Bevels.  The  bevel  in  the  angle  at  M  gives  the  cut  for  the 
foot  of  the  long  hip  VK;  and  the  bevel  shown  at  0  gives  the 
dowu  cut  for  the  long  hip;  the  bevel  at  N  gives  the  cut  for  the 


Plate  49.  217 

foot  of  short  hip,  and  the  bevel  shown  at  V  gives  the  down  cut 
for  the  short  hip.  For  ail  the  common  and  also  the  jack  rafters, 
the  Ltevf  1  at  P  gives  the  foot  cut,  and  the  bevel  at  Q,  gives  the 
down  cut. 

Pig.  3.  [Scale  %''— 1  foot.]  Shows  a  practical  method 
to  get  the  side  cut  of  jack  rafters  against  the  long  hip  BK,  Fig.  1. 

A  indicates  tlie  rafter  having  the  foot  cut  to  suit  the  raising 
plate;  Vindicates  the  "sole"  of  rafter  turned  up,  and  the  bevel 
found  in  the  angle  at  9,  Fig.  1,  is  drawn  across  the  ''foot  cut,"'  as 
2  3;  Ihen  at  right  angles  to  the  foot  cut  draw  line  from  the  points 

2,  3,  to  intersect  the  upper  side  of  rafter  marked  C,  at  4  and  5; 
connect  4  5  for  the  bevel,  shown;  that  will  give  the  side  cut,  for 
the  jack  rafters  XJ,  XA,  &c..  Fig.  2.  The  rafters  butting  the 
hip  BK,  on  the  opposite  side,  aie  the  same  length  and  have  like 
cuts,  but  made  to  match  those  on  the  opposite  side. 

Fig.  4.  Shmvs  the  side  cut  for  tlie  jack  rafters  butting 
the  iihort  hip  CK. 

A  shows  the  inclination  and  foot  cut  of  jack  rafter;  B  shows 
the  sole  of  rafter  turned  up,  and  the  bevel  found  in  the  angle  at 
8,  on  plan  Fig.  1,  is  drawn  across  the  sole  at  2  3,  from  2  and  3, 
and  at  right  angles  to  the  sole  draw  2  4  and  3  5,  intersecting  the 
top  of  rafter  from  its  opposite  sides,  as  shown  at  C;  connect  5  4 
for  the  bevel  to  cut  the  jack  rafters  shown  at  i/Y"  and  KY,  Fig. 
2;  the  jacks  on  the  opposite  side  of  hip  are  the  same  length  and 
cuts;  the  bevel  for  the  down  cut  is  shown  in  the  angle  at  Q,  Fig. 

3,  for  all  the  jacks  and  common  rafters. 

Fig.  5,  Shows  how  to  get  th:  side  cut  of  long  hip  against 
the  ridge  plate  HG,  Fig.  1. 

A  indicates  the  lower  end  of  hip  rafter;  B  shows  the  foot  cut 
turned  up,  the  bevel  shown  at  10,  Fig.  1*,  is  applied  across  the 
sole  as  2  3.  Draw  8  4  and  2  5  square  to  the  sole,  and  to  intersect 
the  upper  side  of  rafter  marked  C:  join  4  5  for  the  bevel  to  cut 
the  upper  end  of  long  hip  against  the  ridge  plate,  as  required; 
this  bevel  must  be  applied  before  the  backing  is  done. 

The  point  of  hip  rafter  at  6,  is  shown  cut  off  to  the  angle  that 
Ihe  hip  makes  with  the  angle  of  building  at  B,  Fig.  1;  this  gives 
a  point  at  7  on  A  to  set  a  gauge  to  back  the  hip  shown  by  the 
gauge  line  7  8;  this  is  a  practical  way  to  find  the  backing  of  hips. 
No  bevel  is  required  for  backing  the  hip  when  done  in  this  way, 
although  one  is  shown  at  section  H.  f 

Fig.  6.  A  shows  the  lower  end  of  short  hip  CK,  Fia:.  1;  B 
shows  the  sole  turned  up:  C  shows  the  upper  side  of  hip;  the 
bevel  2  3  across  the  foot  cut  is  found  in  the  angle  at  12,  Fig.  1. 
The  bevel  in  the  angle  at  5  gives  the  cut  against  the  ridge  plate 
GK,  Fig.  1,  but  must  be  applied  before  the  backing  is  done;  the 
bevel  in  the  angle  V  gives  the  down  cut;  the  lettering  and  man- 
ner of  finding  the  gauge  line  for  backing  the  hip  is  the  same  as 
shown  at  Fig.  5. 

A  practical  method  to  line  off  the  jack  rafters  is  to  place  the 
number  of  rafters  required  for  one  side  of  hip  on  the  trestles, 

*The  bevels  sliown  at  10  and  12  should  he  t;iken  from  the  angles 
that  the  hips  make  at  their  intersection  with  the  ridge  plate  at  AT, 
as  BKG  and  CKG,  because  the  direction  of  ridge  plate  may  not 
always  be  parallel  to  the  walls,  as  in  this  case. 

+This  method  of  backins  a  hip  was  first  shown  by  Mr.  William 
Paes',  1774,  in  his  Practical  Builder. 


318  Tlatp:  50. 

side  by  side,  and  square  the  oue  end  to  Hue;  set  off  ou  one  side 
from  tlie  squared  eud,  the  length  of  the  shortest  jack,  measured 
to  the  long  point.  On  the  other  side,  measure  off  the  longest  jack 
to  the  extreme  point,  then  use  a  straight  edge  to  connect  the  two 
points,  which  will  give  the  intermediate  lengths  at  the  long  points 
for  each  rafter. 


PLATE  50. 

Plats  50.  Exhibits  how  to  find  the  bevels  for  splayed  work 
on  any  an{jle,  such  as  splayed  jamhs,  boxes,  mill  hopjjers,  pv/r- 
lins,  inclining  posts  or  braces,  struts  and  girts,  in  spire  framr 
Ing,  or  any  cut  in  ivhich  the  mnteritd  is  cdnted  or  raMng,  as  the 
cuts  and  length  of  hip,  valley  and.  jack  rafters,  all  are  obtained 
by  this  principle,  and  should  be  well  studied  by  every  young  man 
in  the  trade. 

Fig.  1.  [Scale  H'^=\  foot].  Shous  how  to  obtain  the  cuts 
for  an  inclining  strut  A,  against  a  post  JB,  and  also  the  foot-cut 
on  the  sill  S;  the  strut  being  canted,  as  shown  on  jilan.  Fig.  2. 
Draw  the  inclination  KL,  for  the  center  of  strut.  Draw  the 
section  CDEF;  draw  the  upper  arris  GH,  parallel  to  the  center 
line  LK;  with  JS  as  a  center,  and  EF  tor  a  radius,  draw  the  arc 
FJ;  draw  a  line  parallel  to  HG,  to  tangent  the  arc  at  J,  as  shown 
by  the  dotted  line.  From  iif  and  G,  draw  lines  at  right  angles  to 
GH,  intersecting  the  dotted  line  at  3  au<l ;;;  join  -1  K  and  3  L  for 
the  bevel  required- 
Pig.  3.  Shows  the  same  principle  applied  to  the  upper  end  of 
an  inclining  post;  the  bevel  is  found  in  the  same  manner  as  at  the 
foot  of  the  inclining  strut.  Fig.  1,  the  lettering  being  the  same. 

If  the  post  be  ou  a  corner  and  the  strut  on  an  angle,  and  the 
arris  GH,  Fig.  1,  is  required  to  be  backed,  then  to  find  tlie  angle 
of  backing,  turn  up  the  foot  cut  as  shown  at  A.  Fig.  3,  and  draw 
the  angle  of  plan  as  4  o  5;  continue  the  side  4  3  to  intersect  the 
side  5  (3  at  7;  then  set  a  gauge  from  the  a  iris  HG,  Fig.  1,  to  cut 
the  point  7  lor  the  line  of  backing.  If  the  angle  of  plan  be 
acute  or  obtuse,  then  make  the  augle  4  ;3  5,  Fig,  2,  agreeable  to 
the  plan.  In  the  above  case  the  angle  is  shown  on  the  foot  cut 
as  a  right  angle. 

^  Fig.  4.  Slwv)8  hotv  to  find  the  side  cuts  for  fplaycd  Jamb 
easing,  or  soffits,  the  angles  being  eitfier  square,  acuts  or  obtuse 
on  pUtn. 

A  and  B  are  square  angles,  C  an  acute,  aud  D  shows  an  ob- 
tuse angle.  ABCD,  EFGH  show  the  plan;  BH  and  AE 
show  the  square  miter  on  plan;  CG  sliows  the  miter  on  plan  for 
the  acute  angle,  and  DF  ihe  miter  on  plan  for  the  obtuse  angle; 
./"if  shows  the  inclination  or  splay  required,  aud  equals  the  width 
of  splayed  work. 

From  the  points  E,  F,  G,  H,  draw  peipendieulars  to  EF, 
FG.  GH,  and  HE;  set  off  the  width  of  splay  JK,  parallel  to 
AD,  DC,  CB  aud  BA,  to  intersect  the  perpendiculars  at  2,  3, 
4.  5,  6,  7  and  8;  connect  8  B,  7  B,  6  C,  b  C,  i  D,  3  D  and  2  A 
for  the  bevels  required  to  cut  the  ends  of  splayed  work,  as 
shown  for  their  respective  miters.  If  the  ends  are  to  be  mitered, 
or  a  butt  joint  be  required,  then  proceed  as  directed  at  Figs.  5, 
15,  7  or  8. 


Plate  50.  aifl" 

Pig.  5.  Shows  h(no  to  proceed  in  obtaining  the  three  dif- 
ferent bevels  that  maybe  required  for  a  right,  obtuse  or  acute 
iingle  for  a  splayed  box  or  hopper. 

JK  iuclicates  the  splaj-  giveu  to  the  side  of  box,  aud  agrees 
with  the  splay  JK,  Fig.  4,  the  upper  edge  KA  being  square  to 
JK,  aud  equal  to  the  thickness  of  stuff.  Draw  the  horizontal 
line  AB.  draw  the  perpendicular  line  KL  indefinite,  and  cut- 
ting AB  at  C.  With  K  for  a  center  aud  KA  as  u  radius, 
draw  arc  AX  indefinite;  again,  with  K  for  a  center  and  KB  for 
a  radius,  draw  the  arc  BY  indefinite. 

Now  the  two  right  angle  triangles  ACK  aud  BCK  form 
the  base  for  all  the  bevels  that  may  be  required.  If  the  splay 
was  equal  to  an  angle  of  45  degrees  from  a  horizontal  plane,  then 
only  two  bevels  would  be  required;  for  then  the  perpendicular 
CK  would  divide  the  right  angle  triangle  AKB  equally,  and 
the  bevel  for  the  side  cut  would  also  apply  for  tlie  butt  cut,  be- 
cause the  two  inclinations  AK  and  KB  would  be  alike,  as 
shown  at  EDCF  for  Fig.  1. 

Fig.  6.    Shows  the  bevels  for  an  obtiise  angle. 

Let  KF  and  FG  indicate  the  side  of  box,  aud  FD  the  miter 
on  plan  corresponding  to  FD,  Fig.  4;  prolong  DF  to  the  left; 
now  from  the  points  A  and  B,  Fig  5,  draw  lines  parallel  to 
KL  indefinite,  euttiug  the  ndter  FD,  on  plan  Fig.  6,  at  2  and  a. 
Again,  draw  lines  to  tangent  the  arcs  at  X  aud  Y,  Fig.  5,  and 
parallel  to  KL,  as  shown  by  the  outside  dotted  lines;  from  -J  and 
parallel  to  the  side  of  box  GF,  draw  2  4;  draw  3  5.  3  0  and 
4  7,  all  at  right  angles  to  KL;  connect  Fo,  FQ  and  F7  for  the 
bevels. 

The  bevel  shown  in  tue  angle  at  J?'  is  for  a  butt  cut;  the  bevel 
in  the  angle  at  6  is  for  the  miter  at  the  ends;  and  the  bevel  shown 
in  the  angle  at  5  is  for  the  side  cut,  aud  is  the  same  as  shown  in 
the  angle  at  3,  Fig.  4. 

Fig.  7.     Shows  the  bevels  lohen  angle  on  j^lnn  '■'<  'n'ufe. 

Let  FG  aud  GH  indicate  the  sides  of  box.  and  GC  the  miter 
ou  plan  which  corresponds  to  GC  on  plan,  Fig.  4.  Prolong  the 
dotted  lines  from  A.  B  and  X.  y.  Fig.  5,  parallel  to  LK:  the 
lines  from  A  and  B  cut  the  miter  on  plan  at  2  aud  3.  From  2. 
and  parallel  to  the  side  of  box  GH.,  draw  2  4;  draw  2  5.  3  (>  aiid 
4  7  all  perpendicular  to  the  center  line  KL;  join  G  .">,  G  G  and 
G  7  for  the  bevels.  The  bevel  in  the  angle  at  5  is  the  side  cut. 
and  is  the  same  as  shown  in  the  angle  at  6,  Fig.  4.  Tiie  bevel  in 
the  angle  at  G  gives  the  butt  cut,  aud  the  bevel  in  the  angle  at  6 
gives  the  miter  cut  if  required. 

Fig.  8.  Shoi'-s  the  bevels  when  the  angle  on  jylan  is  a  right 
angle. 

Let  GH  and  HE  indicate  the  sides  of  box,  and  HB  the 
miter  on  plan  corresponding  to  HB  on  plan.  Fig.  4.  Ohseive  the 
dotted  lines  that  are  drawn  from  the  points  A  and  B,  Fig.  5; 
parallel  to  the  center  line  KL,  intersect  the  miter  BH on  plan  at 
2  and  3;  from  the  points  2  aud  3,  draw  lines  at  right  angles  to  the 
center  line  KL  to  intersect  the  outside  dotted  lines  at  5,  7  ami  6; 
draw  JEf  5,  H6  and  iJ7  for  the  bevels.  The  bevel  in  the  angle 
at  5  gives  the  side  cut,  aud  is  the  same  as  shown  iu  the  angle  at 
7,  Fig.  4.  The  bevel  iu  the  angle  at  H  gives  the  butt  cut,  and 
the  bevel  in  the  angle  at  6  gives  the  miter  cut  if  required. 

"  The  student,  by  a  diligent  study  of  these  eight  figures,  may 
find  the  cuts  for  any  splay. 


•330  Plate  50, 

f'igs.  9  and  10.  Show  how  to  find  the  veneer  for  a  cir- 
cular  door-head  having  splayed  jambs;  the  splay  being  carried 
around  the  head  agreeable  to  the  jambs. 

Fig.  9.     Shows  the  plan. 

AB  and  CD  show  the  splay  of  jambs.  Prolong  AS  and  CD 
to  converge  at  O:  with  O  for  a  center,  and  OD  and  OC  as  radius, 
draw  the  arcs  DE  and  iJi^' indefinite. 

rig.  10.    Shows  the  elevation  of  arch. 

BD  is  the  lesser  diameter,  and  corresponds  to  BD,  on  plan, 
Fig.  y.  From  the  center  O,  draw  the  semi- circle  BCD;  with  the 
dividers,  divide  the  semi-circle  into  11  equal  parts,  as  1,  3,  3,  &c. 

Now  return  to  plan,  Fig.  1,  and  with  the  dividers,  step  off  on 
the  arc  DE,  the  same  number  of  equal  spaces,  as  1,  2,  3,  &c.,  to 
H:  draw  the  radial  line  OH  to  J  for  the  length  of  veneer 
DEHJFC  required. 

This  veneer  is  made  from  thin  slutf  and  bent  over  a  semi- 
conical  drum  made  to  the  lines  AOC,  then  tapered  staves  glued 
on  the  back,  and  cleaned  off  afterwards,  thin  strips  may  be  glued 
on  the  back  to  stiffen.  The  radial  lines  from  O,  will  give  the 
taper  for  the  staves,  as  shown  at  EF\  lor  painted  work,  the 
tsplayed  head  may  be  glued  up  with  staves. 

For  the  joint  bevel  of  staves,  draw  the  two  staves  ab.  dc. 
Fig.  10.  Draw  the  radial  line  ob:  return  to  Fig.  9,  make  Kb 
equal  Ob,  Fig.  10;  draw  ba  parallel  to  OC;  from  K,  and  at 
right  angles  to  ba,  draw  Kc;  return  to  plan,  from  O,  and  per- 
pendicular to  Ob,  draw  a  line  indetinite;  prolong  the  back  of  stave 
be,  to  intersect  the  perpendicular  from  O  at  Z;  make  Of  equal 
Kc,  Fig.  9.  Join  fZ,  and  the  angle  at  /,  gives  the  joint  bevel 
for  the  staves. 

Pigs.  11  and  12.  Shows  the  above  jyrinciplc  applied  to 
the  con8tructlo)i  of  a  sphtyed  "Pue  Bark''  circular  o)i  plan. 

Fig.  11.  Shows  the  plan  of  circnhir  pue.  [Scale  Js'^= 
1  foot]. 

O  is  the  center,  and  OA  shows  the  radius  for  the  intersection 
of  the  back  with  the  seat. 

At  Fig.  13,  J>^  shows  the  splay  of  back.  Prolong  the  incli- 
nation of  the  splay  ED  to  intersect  the  perpendiculars  from  O.  and 
from  the  intersection  (not  shown),  sweep  the  curves  jDi^ and  EH 
indefinite.  Now  divide  the  line  ACE.  Fig.  11,  into  any  number 
of  equal  parts,  as  1,  2,  3.  <kc.  Then  carry  the  dividers  to  the  line 
DF,  Fig.  li,  and  space  off  the  same  number  of  parts  from  D  to- 
wards F:  from  the  point  of  intersection  (not  shown),  through  F, 
draw  FH:  then  DEFH  shows  the  veneer  that  will  bend  to  the 
curve  ACB,  Fig.  11,  and  at  the  same  time  gives  the  required 
splay  to  the  pue  back.* 

Figs.  13  and  14.  [Scale  38^^=1  foot.]  Shows  how  to 
find  the  curve  of  a  veneer  for  a  circuldr  window  or  door-head  in 
a  circular  wall.  , 

Fig.  13.  Slioios  the  plan;  the  shaded  part  shows  the  cir- 
cular v:all. 

AB,  CD  indicates  the  width  of  opening  in  the  clear,  and 
AC  or  BD  shows  the  width  of  jambs;  draw  the  chords  AB  and 
CD;  perpendicular  to  CD  draw  CE  and  DF;  parallel  to  CD 

*For  a  loug  radius,  use  wire  or  find  three  points  in  the  curve, 
then  apply  the  problem.  Fig.  11,  Plate  2.  Or  from  a  ^i"  scale  draw- 
ing, increase  to  lull  eize  by  ordinates. 


Pl.ATK  51.  22i 

draw  EF.  Bisect  EF  At  0;  from  O  draw  the  semi-circle  EGF; 
space  off  tlie  semi-circle  iuto  auy  number  of  equal  spaces,  as  1,  2, 
3,  &c.;  from  1,  3,  3,  &c-,  draw  lines  parallel  to  CE,  intersecting 
the  chords  at  4,  5,  6,  &c.,  and  7,  S,  9,  &c.:  also  cutting  the  curve 
of  wall  at  2,  2,  2,  etc.,  on  the  convex  side,  and  3,  3.  3,  &q.,  on 
the  concave  side. 

fig.  14.     Shows  Vie  vcnccr. 

Draw  the  base  line  XX  from  A;  set  off  the  spaces  7,  8,9, 
«fec.,  to  equal  1,  2,  3,  Ac,  in  the  semi-circle  E.  G.  F.  Draw  7  4, 
8  5  and  9  6  parallel  to  the  spring  lines  AC  and  BD. 

Make  7  3,  8  3,  9  3,  and  4  2,  .5  2,  (5  2,  itc,  equal  corresponding 
spaces  on  ordinates  Fig.  13;  then  trace  the  curve  through  the 
points  C,  2,  2,  2,  etc..  for  the  convex  side,  and  through  the  points 
A,  3,  3,  3,  &c.,  for  the  concave  side  of  veneer,  being  careful  to 
tangent  the  straight  part  at  the  spring  lines  AC  and  JBD.  The 
veneer  may  be  bent  over  a  drum  and  staves  glued  on  the  back. 
The  staves  should  be  made  from  very  dry  material,  and  so  for  all 
work  in  which  glue  is  used. 


PLATE  51. 

Plate  51.  Exhibits  hoio  to  find  the  angle  anljack  rihsfor 
an  arched  ceiling  in  a  recess  back  of  a  pxilpit;  and  also  hoiv  to 
find  the  angle  brackets  for  a  stucco  cornice. 

Pig.  1.  [Scale  K'^=l  foot].  Shows  (he  plan  of  arclied 
celling. 

The  shaded  part  shows  the  jambs  of  proscenium  arch;  AB 
and  JBC  indicate  the  seats  of  angle  rib  or  "groin";  EB  and  FB 
show  tlie  seat  of  side  ribs,  the  curve  of  which  is  determined  from 
the  main  rib  EB;  divide  AG  iuto  6  equal  parts;  also  divide  AE 
into  (j  equal  parts;  8  J"  and  J  3  show  the  seats  of  jack  ribs. 

Fig.  2.    Shows  the  elevation. 

Draw  the  base  line  XX  indefinite.  Make  BE  and  BF  equal 
B^aud  BF,  Fig.  1;  make  BA  equal  the  seat  of  angle  rib  BA 
on  plan,  Fig.  1.  From  B  and  A,  erect  perpendiculars  indefinite; 
JBJkf  is  the  height.  From  M,  draw  a  line  parallel  to  XX,  to  in- 
tersect the  perpendicular  from  A,  at  R;  with  (S/S  for  centers, 
draw  the  segments  EPM  and  FQM  for  the  main  arch  back  of 
the  proscenium  arch.  Divide  EB  into  6  equal  parts,  as  3,  2,  3, 
&c.;  also  divide  jRJlf  into  6  equal  parts,  as  3,  3,  3,  &c.  From  2. 
3,  3,  Ac,  erect  perpendiculars  to  XX,  to  intersect  the  arch  EPM 
at  4,  4,  4,  &c.  From  4,  4,  4,  &c.,  draw  horizontal  lines  to  inter- 
sect perpendicular  lines  from  the  points  3,  3,  3.  Ac,  at  C,  C,  C,  &c. 
Through  A,  C,  C,  Cand  M,  draw  the  curve  for  the  angle  rib  or 
groin;  if  another  point  is  required  between  A  and  C,  tlien  bisect 
the  space  .E73  and  R  3,  and  draw  the  perpendicular  and  horizontal 
lines  as  before,  and  as  shown.  Then  ACC-M  is  the  angle  rib 
for  the  seat  line  AR  on  plan,  Fig.  1,  and  will  agree  with  the  main 
rib  EPM  when  in  position. 

For  the  side  rib  BG  en  plan.  Fig.  1,  to  agree  with  the  angle 
rib.  Make  BG  equal  BG  on  plan,  Fig.  1;  draw  GTparallel  to 
BM;  divide  MT  into  6  *  equal  parts,  as  5,  5,  5,  &c. ;  from  5,  5,  .5, 

*The  number  of  points  may  be  more  or  less.    Tlie  greater  thu 
number  ol  points  the  more  correct  the  curve,  will  be. 


2S2  Pr.ATF.  51. 

let  fall  perpendiculars  to  intersect  horizontal  lines  from  4,  4,  4,  &c., 
at  D,  D,  D,  &Q.  Through  M,  D.  D,  D  and  G,  draw  the  curve 
for  the  side  rib  that  will  agree  with  the  angle  rib  ACC-M;  if 
another  point,  H,  is  required  between  G  and  D,  tlien  bisect  5  T, 
and  draw  lines  as  before. 

Extend  the  horizontal  lines  to  intersect  the  main  arch  FQM 
at  6,  7,  8,  &c:  from  the  points  6,  7,  8.  9,  draw  perpendiculars  as 
shown  by  the  dotted  lines  6  i,  or  y  N.  Then  FQ  9  is  the  jaclc 
rib,  to  agree  with  J"  8,  on  plan  Fig.  1,  less  the  halt  thickne.-s  of 
angle  rib;  9  iV"  is  tiie  vertical  cut,  and  the  butt  cut  against  the 
angle  rib  may  be  found  in  a  practical  way,  as  shown  for  the  cut 
at  6  L. 

From  the  intersection  of  the  two  sides  of  jack  rilj  with  the 
angle  rib  Fig.  1,  draw  a  and  b,  at  right  angles  to  8  J;  then  make 
6  a.  Fig.  2,  equal  ab.  Fig.  1;  draw  ab  parallel  to  6  L;  now  set 
off  the  thickness  of  jack  rib  as  KJ.  parallel  to  the  upper  side  of 
rib,  and  draw  Ld  and  be  to  the  opposite  sides  of  rilj;  then  con- 
nect de  for  the  bevel.  Mind  the  exact  length  of  jack  rib  is  the 
the  half  thickness  of  groin  rib  less  than  the  cut  here  shown,  meas- 
ured square  from  this  cut. 

The  distance  cd,  on  plan  Fig.  1.  is  to  be  taken  from  the  jack 
J" 3,  and  shown  at  DV,  Fig.  2:  GDV  shows  the  length  of  jack 
rib  less  the  half  thickness  of  angle  rib,  which  agrees  with  JZ  on 
plan  Fig.  1.  These  ribs  may  be  made  in  two  thicknesses  of  \}i" 
plank,  and  allowed  to  lap  at  the  joints. 

For  the  bevels  at  the  upper  end  of  angle  ribs,  return  to  plan 
Fig.  1.  From  t  and  S,  and  at  right  angles  to  the  seat  BA,  draw 
tg  and  sf;  also  from  n  and  r,  and  perpendicular  to  the  seat  BA, 
draw  nJ  and  rh;  make  Mb.  and  Mf.  Fig.  2,  equal  fg,  and  jh, 
Y\g.  1;  draw  izj"  and /£•  parallel  to  MB:  let  ZZ  equal  the  incli- 
nation and  thickness*  of  groin  at  the  upper  end;  draw  go.  jn 
and  MS  at  right  angles  to  the  inclination  of  groin,  as  shown. 
Join  OS  and  NS  for  the  bevels  required. 

Fig.  3.     Shows  a  common  bracket  for  a  jilastcr  cornice. 

AB  is  the  projection  along  the  ceiling,  and  AC  is  the  dis- 
tance down  the  wall.  From  the  projections  and  curvature  of 
bracket,  as  1,  1,  1,  &c.,  draw  perpendicular  lines  to,  and  intersect 
AB,  as  2,  2,  2,  &c. 

Fig.  4.  Shows  the  seat  DE,  of  angle  bracket  for  a  right 
angle  ADF;  how  to  find  the  curve  for  the  angle  bracket  to  agree 
with  the  common  bracket.  Fig.  3.  From  tiie  points  2,  2,  2,  Fig. 
X,  draw  lines  parallel  to  AD,  intersecting  DE  At  3,  3,  3. 

Fig.  5.  Shows  the  angle  bracket.  Draw  the  right  angle 
CDE;  make  D,  3,  3,  3-.B,  Fig.  5,  equal  D,  3,  3,  3-^,  Fig.  4. 
Make  DC,  3  1,  3  \—E  1,  equal  AC,  2  1,  2  1,  2  l-B  1,  Fig.  3,  then 
trace  the  contour  of  bracket  through  the  points  1,  1,  1,  I,  as 
shown. 

Fig.  6.  Shows  the  seat  KH  for  an  obtuse  angle  AKD,  the 
projection  CD,  being  the  same  as  at  Fig.  3.  How  to  find  the 
trace  of  angle  bracket.  With  KH  for  a  radius,  and  any  point  on 
AD,  Fig.  3,  for  a  center,  as  K,  draw  arc  at  H;  join  KH,  cutting 
the  perpendiculars  from  AB,  Fig.  3,  at  4,  4,  4. 

Fig.  7.     Shoivs  the  angle  bracket. 

Draw  the  right  angle  CKH;  make  K,  4,  4,  i-H  equal  K,  4, 
4,  4l-H,  Fig.  7.     From  4,  4,  i-H,  draw  perpendiculars  to  KH 

*  Remember  the  thickness  of  the  angle  rib  must  equal  that  on 
n)an. 


Pi,ATK  51.  S2S 

Inrlefinite.  Now  raako  KC.  4  1,4  \-H  1,  equal  AC,  2  1,  2  1— J3 
1,  Fig.  3,  and  trace  the  profile  of  bracket  through  the  points  C.  1, 
1,  1,  &c. 

Pig.  8.  Shiivn  the  sent,  KL,  of  an  angle  J/vachiet  for  an 
acute  anrilc,  ALB. 

Tlie  projection  CA  agrees  with  AB,  Fig.  3;  how  to  find  the 
trace  of  angle  bracket.  With  KL  as  a  radius,  and  K,  Fig.  3,  for 
a  center,  draw  arc,  cutting  BB  at  L;  join  KL,  cutting  the  per- 
pendiculars at  5,  5,  5,  «fec. 

Pig.  9.     Shores  tlie  avijle  brachct. 

Draw  the  right  angle  CKL  indefinite;  make  K  5  o-L  equal 
K.  ~),  5,  5  L.  Fig.  3.  From  5,  .5,  5-i,  draw  perpendiculars  to 
KL  indefinite.  Make  KC,  5  1,  5  1,  .5  l-I,  I  equal  AC,  2  1,  2  1- 
B  1.  Fig.  3;  then  trace  the  outline  of  bracket  through  the  points 
C,  1,  1,  1.  &c. 

These  angle  brackets  may  be  cut  out  square  to  the  face  of  plank, 
and  tlie  lath  allowed  to  joint  at  the  center  of  bracket  for  internal 
angles;  for  external  angles,  the  two  outside  corners  have  to  be  taken 
off  to  the  center  of  bracket,  that  the  lath  may  miter  and  nail  solid. 


2^4  Mechanioax.  Cabpentrt, 


Mechanical  Carpentry. 


Transverse  strength  of  rectangular  wooden  beams. 

The  transverse  strength  of  rectangular  wooden  beams  is  in  pro- 
portion to  the  breadth,  by  tlie  square  of  the  depili,  and  inversely 
as  the  length.  Rule— multiply  the  breadth  by  the  square  of  the 
depth  in  inches,  and  that  product  by  the  constant  for  the  kind  of 
material  required;  then  divide  by  the  length  between  the  supports, 
in  feet,  for  the  breaking  weight  in  pounds. 

Formulated  thus:    JB= y. 

JB  equals  the  breaking  weight  in  pounds;  b  equals  the  breadth, 
and  d  equals  the  depth,  both  in  Inches;  L  equals  the  length  in 
feet  between  the  supports;  C  equals  a  constant  found  by  experi- 
ment tests  on  a  unit  of  material,  by  taking  a  bar  one  inch  square 
and  ly^  long  between  supports,  and  loading  the  bar  at  the  center 
until  it  breaks.  The  weight  that  breaks  the  bar  is  termed  the 
"constant"  for  that  kind  of  material. 

The  unit  of  material,  when  of  hemlock,  breaks  with  4.50  lbs.; 
white  pine  500  lbs.;  spruce  550  lbs.;  white  oak  6.50  lbs.;  Georgia  yellow 
pine  850  lbs  ;  locu.st  1,200  lbs.;  cast  iron  2,;500  lbs.:  wi'ought  iron  2,600 
lbs.;  and  steel  breaks  with  a  load  of  0,000  Ihs.— Hatfield. 

Pig.  7.  Plate  49  indicates  a  white  pine  joist  ^^  by  10^'' 
deep.  The  length  between  the  supports  AB  equals  16^,  required 
the  breaking  weight,  with  the  load  at  the  centei-. 

_     bd^'C    2^'XIO^'XI 0^^X500 
Formula:  B=—j^  = =^^7 =6,250  lbs, 

equals  6250  lbs.  The  young  man  sliould  study  this  first  formula 
well,  for  the  breaking  weight  of  material  subject  to  a  cross  strain. 
It  is  a  wfU-known  fact  that  if  the  weight  be  uniformly  di.s- 
tributed,  as  at  Fig.  8,  the  load  may  be  doubled  on  the  beam,  or 
equal  to  12,500  lbs.,  and  the  formula  wouhl  read 

_     2db'^C     2X3^'X10'^X10''X-'>00 
B:=—j^=-^~- ^g,     ^- =12,500  lbs. 

It  is  also  proven  from  experiment  that  if  the  same  beam  be 
firmly  fixed  at  one  end  ;md  weiehted  at  the  free  end,  as  shown  at 
Fig.  9,  the  breaking  weight  would  equal  one-fourth  the  first  ex. 

ample,  or    ""*    =^1562.5  lbs.,  and  the  formula  would  read 
4 

„    bd^C    2^'X10'^X10'^X500 

^=-4'L  =-  4X1*3- -'^'''■'  ''''• 

And  for  a  uniformly  di.stributed  load,  as  .shown  at  Fig,  10 
would  be  doubled,  or  equal  to  3125  lbs. 

It  is  al.so  a  fixed  rule  that  if  the  beam  be  firmly  fixed  at  both 
ends  and  weighted  at  the  center,  as  shown  at  Fig.  11,  then  the 


Mechanical  Carpentry  336 

breaking  weight  would  be  one  and  a  half  times  the  first  example, 
or  9375  lbs.,  and  the  formula  would  read : 

JB= j^ = ^^7 =9,375  llw., 

and  the  uniformly  distributed  load,  as  shown  at  Fig.  12,  would 
be  doubled,  or  equal  to  18,750  lljs. 

If  the  beam  be  firmly  fixed  at  one  end  and  supported  at  the 
other,  as  shown  at  Fig.  13,  then  the  breaking  weight  would  equal 
1}X  times  the  first  example,  or  7812  lbs.,  and  the  fonuula  would 
read: 

1 H  bdPC      13^X2''X10''X10''X500  lbs. 
Br= j^ = jgT  =-7,813  Ih->. 

and  the  uniformly  distributed  load,  as  shown  at  Fig.  14,  would 
be  double,  or  equal  to  15,634  lbs. 

The  foregoing  rules  as  set  forth,  are  for  the  breaking  strength 
of  timber,  and  are  established  from  the  average  of  several  tests 
made  on  each  kind  of  wood;  the  bars  selected  for  the  tests  are 
supposed  to  be  perfect,  or  nearly  so,  hence  a  factor  of  safety  is 
reouired  to  avoid  accident. 

Mr.  G.  Hatfield  puts  the  factor  of  safety  for  the  above 
formula  at  3  and  4;  The  New  York  building  laws  also  provide 
a  factor  of  3  for  safety.  Valuable  data  has  recently  been  added 
to  the  transverse  strength  of  timber  by  Professor  Lanza  and  his 
students  at  the  Massachusetts  Institute  of  Technology.  They 
experimented  on  full  sized  timbers,  and  made  the  discovery,  that 
the  usual  factor  3  for  safely  is  too  low  for  the  j*?neral  run  of 
timber  as  supplied  from  the  mills  and  yards.  The  knots  proved 
to  be  the  weakest  part  of  the  timber.  A  factor  of  6  will  nearly 
harmonize  Mr.  Hatfield's  formula  with  Prof.  Lanza's  experiments. 

Then  if  the  breaking  weight  in  the  first  example  be  divided 
by  6,  the  result  will  be  the  safe  or  working  load  for  the  timber. 

The  formula  would  then  read  : 

equals  1,041  lbs.  for  the  safe  load  concentrated  at  the  center  W, 
Fig.  7.     And  the  unifonnly  distributed  load  would  be  doubled,  or 

equal  to  2082  lbs,;  the  formula  would  read  :     S=^-J^^ 

S  equals  safe  load. 

The  safe  load  for  the  same  beam  firmly  fixed  at  one  end  and 
leaded  at  the  free  end,  as  shown  at  Fig.  9,  the  formula  would  read; 

^    bd^C   2^^X10'' X10^"X500    ,,,,,  „ 

^-476ir — Ixexre"    "^''"  ^'''•= 

and  the  unifoimly  distributed  load,  Fig.  10,  would  equal  twice 
that,  or  520  lbs.  for  a  sale  load. 

And  the  safe  load  for  the  beam  Fig.  11,  firmly  fixed  at  both 
ends  and  load  at  the  center,  would  be  formxUated  thus  : 

«    iHbd^-C     ii/X3"Xlo"Xlo"X500     ,  ,^, .  „ 
8^—Q-^-- ^n^^, -==1..62  o  lbs.; 


226  Mechanical  Cakpextry. 

and  for  the  uniforrrflj'  distributed  load,  Fig.  12,  the  safe  load 
would  be  twice  1562  lbs,  or  3125  lbs.;  aud  tlie  formula  would  be  ; 

The  safe  load  for  the  beam,  Fig.  13,  firmly  fixed  at  one  end 
aud  supported  at  the  other,  is  fonnulated  thus  : 

IH  bd^C      iKX3'^Xio''Xio^'X500 
^=~-6~ir~= 6Xl6^ ^ =1'203  lbs. 

equals  1,303  lbs.  And  the  uniformly  distributed  load,  Fig.  14, 
would  be  twice  1,302,  or  equal  to  2,601  lbs.  for  the  safe  load. 
Formulated  thus: 

2,iHbd^'C   2X13^X2^"  Xio^^XiQ^^XSOO    „  ^„,  ,^ 
S^ >^l, = 6X16'>^ ^^'^^^  ^^^- 

The  best  form  for  rectangular  beams  is  when  the  proportion  of 
the  breadth  Is  to  the  depth,  (or  nearly  so),  as  5  is  to  7;  as  for  ex- 
ample 3"X4"  scantUng,  4"X6".  e"X8",  8"X10",  9"X12",  10"X14"  timbers. 

How  to  find  the  reaction  at  the  walls,  when  a  load  is  concen- 
trated at  any  point  other  than  at  the  center  of  the  beam.  Of 
course,  if  a  beam  be  loaded  at  the  center,  as  at  W,  Fig.  7,  one-half 
the  load  is  transmitted  to  each  of  the  supports  A  and  JB,  and  the 
reaction  at  each  of  the  supports  isequal  to  one-half  the  load  at  W; 
but  if  the  weight  be  changed  towards  either  end,  then  the  reaction 
at  the  walls  will  be  in  the  inverse  proportion  to  its  distance  from 
each  end. 

Fig.  7,  Plate  49.  Shows  a  beam  16' 0'^  between  supports. 
Load,  say  100  lbs.  at  C,  4'  0'^  from  the  support  at  A;  required  the 
reaction  at  the  supports  A  and  JB.  * 

Rule.  Multiply  the  weight  at  C  (100  lbs.)  by  the  distajice  to 
the  near  support  (4''  0''-'),  and  divide  tbe  product  by  the  length 
AB  (16''  0"),  for  the  reaction  at  B;  then  subtract  tiie  reaction  at 

100V4''  O" 
B  from  the  total  load,  for  the  reaction  at  A.    Thus  —  ,    .,    :=r 

16'  0" 
25  lbs.  that  are  transmitted  to  the  support  B;  then  100  lbs.  minus 
25  lbs.  (100—25=75  lbs.)  equals  75  lbs.  carried  to  the  near  sup- 
port A. 

Again,  suppose  the  beam,  Fig.  15,  to  be  loaded  at  three  dif- 
ferent points  C,  D  aud  E.  AB  equals  16'  0";  AC  equals  4^0"; 
Ai>  equals  7'  0";  AjE7  equals  10'  0",  from  the  near  support  A. 
The  weights  C,  D  aud  E,  equal  150,  200  and  900  lbs.  respectively, 
or  1,250  lbs.  for  the  total  load,  exclusive  of  the  beam.  Proceed 
as  before,  and  find  the  reaction  at  the  remote  support  B  for  each 
weight,  separately;  then  add  the  results  togetlier  and  subtract 
that  sum  from  the  total  load,  for  the  reaction  at  the  near  support  A. 

4'  O'^XfSO 
Thus  A C=      . ft77)7/ — "^37.5  lbs.  for  the  reaction  at  B. 

n'  0'''X200 
A.P— — ■,^/  n// — —87.5  lbs.  for  the  reaction  at  B. 
lo'  0" 

10'  0"'X900 
A.ff= — .g/  Q// — =562.5  lbs.  for  the  reaction  at  B. 

*  A  cipher  is  here  added  to  denote  inches.  If  inches  should 
occur  in  any  of  tliese  calculations,  then  reduce  the  inches  to  the 
decimal  of  a  foot,  to  facilitate  calculation.  For  instance,  should  the 
measurement  be  4'  9",  then  tlie  item  would  read,  four  feet  and 
seventy-five  hundredths  [4.75']. 


MECHAXTfAT,   CARPENTRY.  23T 

Then  37.54-87.?>-|-562.5  equals  687.5  lbs.  of  the  weight  car- 
ried to  the  supviort  B:  hence  the  amount  carried  to  the  support  A 
equals  the  weights  C,  D,  E,  150^200+900=1250  lbs.,  minus 
the  total  reaction  at  the  support  B.  Thus,  1250—687,5=563,5 
for  the  total  reaction  at  support  A. 

In  the  above  calculation  the  weight  of  beam  has  not  been  con 
sidered.    One-half  the  weiglit  of  beam  should  be  added  to  each  total 
reaction. 

This  problem  is  useful  to  the  mechanic  when  framing  around  the 
well  of  stair-ways  and  stcylijihts  where  one  trimmer  raay  have  to 
support  several  concentrated  weights. 

Strains.  Rule — Tlie  strain  or  bending  moment  at  any 
point  in  a  beam  is  equal  to  ti.e  reaction  at  the  support  multiplied 
by  its  distance  from  the  pouit  selected.  The  weight  at  the  center 
of  beam,  Fig.  11,  equals  say  200  lbs.  Then,  of  course,  the  reaction 
at  the  supports  A  and  B  equals  100  lbs.  pins  the  half  weight  of 
beam  or  trimmer;  then  let  be  required  to  find  the  strain  at  the 
point  D.  the  reaction  at  A  equals  100  lbs. 

Thus,  AB  equals  8^0^^;  then  8^^X100=800  lbs.  for  the  strain 
at  the  point  D,  for  a  single  load. 

Find  the  strain  at  the  point  C,  3^  0'^  from  the  support  A; 
AC  equals  3''  0^^;  then  3.0 :<100  ]bs.=300  lbs.  as  the  strain  at  the 
point  Cfrora  the  single  load  at  D. 

Find  the  strain  at  the  point  E;  BE  equal  5'  0'^\  then  b'  d'^ 
XlOO  lbs.=:500  lbs.  as  the  strain  at  point  E  from  the  single  load. 

Let  it  be  observed  at  Fig,  11  the  weight  is  at  the  center  of 
beam,  and  the  strain  is  found  at  any  other  point  from  the  reaction 
at  the  supports.  At  Fig.  15  three  weights  intercept  each  other 
in  their  passage  to  the  supports.  The  weight  at  C  is  4''  0^^  from 
the  support  A;  the  weight  at  D  is  7''  Q'^  from  A.  and  the  weight 
JE7  is  lO''  O^''  from  the  support  A,  and  the  reaction  at  the  sup- 
port A  equals  562.5  lbs. 

To  ascertain  the  strains  at  the  points  C,  D  and  E,  Fig.  15, 
commence  at  support  A,  Strain  at  C  equals  reaction  at  AX 
A 0=562.5X4'  0^^=2250  lbs. 

Strain  at  D  equals  reaction  at  AX-AjD-Wat  CxCD= 
562.5x7'  0^'— 150x3=3487.5  lbs. 

Strain  at  E  equals  reaction  at  AxAE—W  at  C<CE—W 
at  DXi?^=563.5xlO'— 150x6'  0^^—200X3^  0''=4125'  lbs.  W 
equals  weight* 

The  strain  at  E,  being  the  greatest,  and  the  depth  of  joist 
being  known,  required  the  breath  of  a  white  pine  beam  at  that 
point  to  carry  the  load  safely,  the  beam  being  uniform  through- 
out to  suit  the  width  of  joist. 

The  strain  from  the  concentrated  load  at  E  equals  4125  lbs; 
depth  of  joist  equals  say  12^^;  lengtli  between  supports  equals 
16^  0''.    a,  is  a  factor  for  safety  and  equals  6.     Fonnulated  thus : 

4125  Z,a__4125X16^  0^^X6 
~      Cd^  500X12X12     ~^'  ^' 

equals  SJ'a"  for  the  unknown  breadth  by  12^^  for  the  depth. 

When  floors  sustain  heavy  loads  the  header  that  supports  the 
tail  joist  instead  of  mortise  and  tenon  they  should  be  set  in  stirup 
irons  at  the  joiniug  with  the  trimmers,  and  also  joint  bolts  should 
be  used  and  located  at  the  neutral  axis,  or  center  of  the  timber. 
The  strength  thus  gained  is  from  two  to  three  times  from  the 
stirup  irons  alone. f     Also,  the  tail  joist  shonkl  be  supported  by 

*Wllsou.  ~~~~' 

t  Lanza's  experiments,  American  Archlt-ect  and  Building  News. 


228  Mechanicai>  CAKP^:^rTRY. 

stirup  irons  for  heavy  work.     The  joint  bolts  may  be  omitted  in 
the  tail  joist. 

Posts  and  Struts.  Are  subject  to  compressive  strains. 
The  rule  mostly  followert  is  Mr.  Tredgolds,  mortified  by  Mr. 
Shalor  Smith,  C.  E.,  of  Baltimore.  The  formula  reads  for  square 
or  rectangular  timber  posts  thus  : 

C  <A 


S= 


*'  [^  ^    (-p-X-004)] 


S  equals  safe  load;  C  equals  a  constant  for  the  crushing 
force  per  square  inch,  for  the  kind  of  material  used,  as  shown  at 
table  7:  L  equals  length  of  post  in  inches;  G  equals  tlie  factor 
for  safety;  .004  equals  Mr.  Smith's  constant  for  any  kind  of  ma- 
terial; and  A  equals  the  area  of  cross  section  of  timber;  b  equals 
the  least  dimension  of  the  post  in  inches. 

Example.  Kequired  the  safe  load  for  a  dry  white  oak  post 
8^'  by  10''^  by  9^  or  108^'  long. 

Safe  load= ^^^^^^^ ^70:237  lbs. 

r       ^     108X108  -, 

6[l*(-SX8-><«04)] 

equals  70,237  pounds  as  safe  load.  Observe  that  if  the  post  sup- 
ports a  beam  of  white  pine,  the  upper  end  of  post  must  have  a 
bolster  or  pillow  of  some  hard  wood,  or  else  the  post  would  sink 
into  the  pine  girder,  as  shown  at  column  5,  table  7,  where  tiie 
shearing  force  across  the  grain  per  square  inch  for  white  pine  is 
800  pounds,  and  the  area  of  cross  section  of  post  equals  80  square 
inches.  Tlien  80X800=64,000  pounds,  allowed  to  crush  the 
girder  ^^  of  an  inch;  hence  the  post  should  be  capped  with  an 
oak  bolster'^'  projecting  a  foot  on  each  side.  The  effect  of  the 
post  on  the  oak  bolster  from  the  load  of  70,237  pounds  would  be 
immaterial,  as  seen  from  column  six,  table  7,  wheie  1060  pounds 
is  allowed  per  sipiare  inch  for  a  sensible  impression.  Hence, 
1060X80=84,800  pounds  as  the  amount  to  load  the  oak  bolster  to 
leave  a  sensible  impression. 

Posts  should  be  carefully  set,  being  plumb  and  well  bedded, 
if  allowed  to  incline;  then  in  addition  to  the  load  they  carrj',  a 
strain  is  set  up  in  the  fibers  that  is  not  provided  for  in  the  dimen- 
sions; hence  accidents  may  occur.  Metal  or  wrought  iron  columns 
set  over  each  other,  their  flanges  should  all  be  trued  up,  being 
centered  in  a  lathe.  It  is  not  safe  to  bed  the  flanges  in  sheet  lead, 
the  lead  is  liable  to  work  an  injury,  especially  under  a  heavy  and 
concentrated  weight. 

For  wood  posts  supporting  heavy  loads,  the  posts  should  have 
metal  caps  and  shoes  in  the  form  of  sockets,  to  receive  the  ends  of 
posts;  the  caps  may  be  recessed  to  receive  the  end  of  the  next 
post,  and  also  project  beyond  the  post  as  a  support  for  the  girder, 
or  a  metal  cap  may  be  fit  down  over  the  end  of  post,  having  two 
sides  continued  up,  forming  a  shoe  to  receive  the  ends  of  girder, 
and  the  metal  sides  forming  supports  for  the  shoe  to  receive  the 
next  post  al)Ove. 

For  warehouses  and  factories,  the  above  construction  will  give 
the  best  satisfaction.  The  end  of  wooden  posts  should  never  b(! 
set  directly  on  a  wooden  girder,  as  the  wood  will  shrink,  often 
more  on  one  side  than  the  other,  thus  cause  the  post  to  deflect  from 

*  Oast  iron  preferred. 


Mechanical.  Cakpentry.  23y 

a  perpendicular,  and  result  in  cracks  in  the  walls,  floors  out  of 
level,  and  fi:ial  ruin  of  tlie  building. 

If  the  posts  or  girders  be  made  from  green  or  part  dry  lumber, 
they  should  be  allowed  to  stand  until  dry  before  paintine.  as  the 
paint  will  close  up  the  pores,  and  thus  prevent  the  moisture  from 
reaching  the  surface;  dry  rot  will  then  commence  at  the  center  of 
timber,  weaken,  and  perhaps  cause  accident.  By  boring  a  hole 
in  the  center  of  the  posts  to  admit  air,  will  prevent  dry  rot;  the 
caps  and  shoes  should  be  cast  with  a  lioHovv  space,  so  as  to  admit 
a  free  circulation  of  air  through  the  post. 

If  posts  be  made  from  green  timber,  the  strength  of  same  v/iil 
be  reduced  one-half:'  therefore  the  constant  for  crushing,  in  No.  -Z 
Column,  Table  7,  should  not  be  taken  at  more  than  one-half. 

Pig.  15,  Plat9  50.  Exhibits  /wio  to  find  tlic  strain  from  a 
load  on  a  brace  or  strut;  the  same  rule  applies  to  a  pair  of  raf- 
t&'s;  and  from  the  strain,  hoio  to  calculate  the  dimensions  of 
timber  required  to  s^ipport  the  load  with  safety. 

Let  AC  and  AS  pass  through  the  center  or  neutral  axis  of 
the  strut  and  tie,  and  SC  equal  the  perpendicular  height,  connect 
the  two  at  the  center  of  timber,  forming  the  triangle  of  forces 
ABC. 

Now  the  length  of  strut  from  center  to  center  of  timbers  is 
10^  0'^.  set  out  6'  O"  from  the  perpendicular  height,  which  is  8' 
0",  a)id  loaded  with  40  tons  at  its  apex;  there  are  two  struts  meet- 
ing at  the  same  point;  therefore  each  strut  has  to  support  20  tons 
each;  required  the  strain  in  each  strut. 

Rule.  As  the  perpendicular  height  {8''  0")  is  to  the  iveight 
{20  tons),  so  Is  the  length  of  strut  ( W  0^^)  to  the  strain  in  the  strut. 

Example:  8'  0":  20::  10: 35  equals  25  tons,  for  the  strain  in 
the  strut  AC. 

Kequired  the  strain  in  the  tie  AB. 

Rule.  As  the  perpendicular  height  {8'  0")  is  to  the  load 
(20  tons),  so  is  the  horizontal,  tie  (6''  u")  to  the  strain  in  the  tie. 

Example;  8'  0^^:25 :: 6'  0"  :15  equals  15  tons,  for  the  strain 
n  the  horizontal  tie  AB. 

Then  25  tons  tiu^  strain  in  the  stnxt  AC  being  reduced  to 
pounds  (2240X25=56,000  lbs.),  equals  5(5,000  pounds,  and  15  tons 
the  strain  in  the  tie  AB  reduced  to  pounds  (2240X15=33,600  lbs.) 
equals  33,600  poimds. 

Required  the  dimensions  of  a  spruce  strut  to  safely  support 
the  compressive  sti'ain  of  56,000  pounds. 

Nov/  from  column  tv>'o.  Table  7,  we  find  the  crushing  force 
per  square  inch  for  spruce  pine  eqiuils  0862,  and  if  we  allow  a 
factor  of  6  for  safety,  or  1000  pounds  per  square  inch,  then 
5^^0q'>|>=56  square  inches  in  section,  or  a  timl)er  7^^  by  8^''  Vv'ill 
give  ample  strength,  provided  the  stiffness  is  sufficient  in  pro- 
portion to  the  length,  for  when  tlie  length  of  a  column  or  strut 
exceeds  15  times  its  least  diameter  there  is  danger  froin  bending. 

Now  to  ascertain  if  the  above  7X8  timber  is  stiff  enough  for 
flexiire,  proceed  by  the  formula  of  Shalor  Smith's  for  the  strength 
of  columns  or  posts,  as  previously  shown.     Thus ; 

6862X56 
Safe  load= — =21,778  lbs. 

e[i+(iHgl!^X.o«4)] 

equals  21,778  pounds,  this  being  too  light ;  try  an  8'^XIO'^  yellow 
pine  timber,  by  the  above  formula,  wliich  will  sustain  a  safe  pres- 
sure of  63,663  pounds ;  this  allows  ample  for  stiffness  of  strut  AC, 

W  lOTlg. 


230  Mechanicai.  Carpentry. 

Next  required  the  dimensiou  of  the  tie  AB  to  safely  resist 
the  tensile  strain  of  33,600. 

From  table  7,  column  3,  we  find  the  tensile  strain  for  a  yellow 
pine  to  be  11,400  pounds  to  a  square  inch,  and  if  we  use  a  factor 
of  6  for  safety,  (1^400=1900),  or  1,900  pounds  per  square  inch, 
then  the  area  of  tie  (33.600-h1, 900=17^),  will  equal  17  square 
inches,  or  a  timber  of  yellow  pine  2X^^X,"i^''  will  be  ample  to  neu- 
tralize the  strain  on  the  tie  AB, 


ALGEBRAIC  SIGNS  AND  SYMBOLS. 

-\-  Plus — Sign  of  addition. 

—  Minus— Sign  of  subtraction. 

X  Times — Sign  of  multiplication, 

-f-  Divided  by — Sign  of  division. 

:  Is  to — Sign  of  ratio. 

: :  So  is — Sign  of  equality  of  ratio  4 : 8  : :  1  fi :  32. 

=  Equals — Sign  of  equality. 

□  Signifies  square  inches. 

[3  Signifies  cubic  inches. 

■\/  Radical  sign  of  square  root, 

f/  Eadical  sign  of  cube  root. 

1  Represents  length. 

b  Represents  breadth. 

d  Represents  depth. 

h  Represents  height. 

-^"i"^    Indicates  the  length  is  to  be  added  to  the  l)readth  and 
d  divided  by  the  depth. 

-^^      Indicates  the  length  to  be  multiplie<.l  by  the  breadth  and 
d  divided  by  the  depth. 

*     "    Indicates  the  breadth  to  be  subtracted  from  tlie  length 

d  and  divided  by  the  depth. 

i-Z)3     Indicates  the  square  of  the  length  is  to  be  multiplied 
by  the  cube  of  the  breadth. 

1    1     Indicates  the  square  root  of  the  lengtli  is  divided  by  the 
f  b  cul)e  root  of  the  breadth. 

l~7bd^  ~ 

\  -^  )  +l=Z.  Indicates  the  breadth  is  multiplied  by  the 
square  of  the  depth  and  divided  by  the 
height  plus  unity,  and  the  square  root  of 
this  sum,  multiplied  by  6,  and  the  pro- 
duct equals  Z. 
[    ]     Bracket — Indicates  that  all  the  figures  within  are  to  be 

taken  together  as  one. 
— —    Bar — Indicates  that  the  figures  over  which  it  is  placed 
are  to  be  taken  together. 


Mkchaxicai,  Cakpentby. 


331 


12"=         ]     ' 

■SQ"=^         'S     '  = 

72"=         6     '  = 

198"==  1(5.5'  = 

r,920"=  660    '=■ 


TABLE  1. 
Long  Mkasure. 


ya. 


1 

a     ••  =     I    fath 
5.5  ••  =     2.75    " 
JO      "  =110        " 
63,360"==5,280    '=1,760      "  =880        "  =320 
1  French  iueter=39. 37  inches. 
1        "      ceutimeter=.about  ?«  of  an  inch. 


Ipch.  or  pole 
40  ••    =lfnr. 

=8  "  =>lml. 


TABLE  2. 
Measure  of  Surface.     (Superficial.) 


144    square  inches  =    1  square  foot. 


9     square  feet 
SO^square  yards 
40    square  rods 

4    square  roods 
640     square  acres 

1     square  mile 


1  square  yard, 
1  square  rod       — 
1  square  rood     =-- 
1  square  acre 


272  >4  square  feet. 
10,890  square  feet. 
43,560 


1  square  acre  =  43,560  square  feet. 
1  square  mile  =27,878,400  square  feet. 
1  square  section,  land  measure. 


1     square==100  sq.  ft.  architect's  aud  builder's  measure 


TABLE  3. 

CfBic  Measure. 

1738       cubic  iriches==      1  cubic  foot. 


27       cubic  feet 

128       cubic  feet 

34.75  cubic  feet 

I       cubic  foot 

1        cubic  foot 

1       cubic  foot 


■=      1  cubic  yard. 

==       1  cord. 

■=■       1  perch  of  etone. 

=2200  cylindrical  inches. 

=3300  spherical  inches. 

=6600  couical  inches. 


TABLE  4. 
Averdupois  Weight. — U.  S.  Standard. 

16  drachms  =1  ounce. 

16  ounces  =1  pound. 

28  pounds  =1  cwt.— L12  pounds. 

4  quarters  or  113  lbs.=l  hundred  weight. 

20  hundred  weight       =1  ton=2340  pounds. 

14  pounds  =1  stone. 

100  pounds  =1  quintal, 

American  Commercial  ton=3000  pounds. 


2?2 


Mechaxicai.  Carpe^ttky. 


TABLE  5. 
Dry  Measi'RE. 
2  piuts=l  quart=67.2  cubic  inches. 
4  quarts=l  gallou=268.8025  cubic  inches. 
2  gallons  ==1  peck=537.605  cubic  inches. 
■i  peck?=l  bushel=2150.43  cubic  inches.       [Winchester.] 


TABLE  6. 

Liquid  Mkasuke. 
4  gllls=:l  piut='.28.875  cubic  inches. 
•2  pints=l  quait.^57.75  cubic  inches. 
4  tiuaits=l  gallon=2ol  cubic  inches. 

<2  a  o  *    r~< 


o 
o 


■It     "HI  ii  u  i,     r^  ,"  rs 


=5  C  co.-.i  7  ^ 


'?a 


P^  I"": 


(■  as  «->  «5  ^ 


.  4) 


«  cH  i  ?  2  «  *: 


55  .    2 


I  a  sd 


g§ 


ri^^ifT-^ 


ht5.r  i: 


'is 


■~  "s 


■*  oc  ^  t>.  o  ;2 

OC  ■*  O  C^  5<>  -H 


-i     a 
■7.£~ 


Ms 


C  3S       o 


C^  W  35 


5.t«a2  .a 

-^  O  3  s      M 


•o  ;c  --I  ^t  -^  —  r;  2  -r  o  o  o 
-» ■*  o  e:  -T  u~_:r  S cr. o  c>o 
— "— '  M '-c'a's-'if:  IS -^  o"oo 


Mechanical  Carpentby. 

TABLE  8. 
Crushing  Strength  of  Building  Material. 


Cru.shing 

Weinht 

Materiai.. 

per 

sq. inch 

in  pounds 

percu. 
foot  in 
pounds. 

Fox  Island  Granite, 

14,875 

Gilmore 

164 

Maine. 

Quincy 

17.750 

" 

\m 

Massachusetts. 

Hurricane  Island  " 

14,425 

** 

166 

Bay  of  Fundy 

11,813 

" 

162 

Joliet,  111.  Limestone 

12,775 

** 

1,58 

Illinois. 

Com.  Italian  Marble 

11.250 

168 

Berea        Sandstone, 

8,300 

133 

Ohio. 

Brown 

9,8;50 

" 

140 

Little  Falls,  N.Y. 

Amherst           " 

6,650 

138 

Ohio. 

Cleveland         " 

6,800 

140 

" 

Massillon 

8,750 

131 

" 

Medina 

17,2.50 
(      375 

150 

New  York 

Brick  (Common), 

\     to 
1   S.O-IO 

Thurston 

113 

Brick-work,  ordin'y, 

300  to  500 

112 

Brick-work,  good  in 

cement,  

450  to  1000 

112 

Press  Brick, 

i2,ono 

Kidder 

Mortar,  common, 

120  to  240 

Haswell 

98 

"           year   after 

setting, 

440  to  580 

Rondelet 

Good  Cement,  pure... 

7,500 

81 

Concrete, 

600 

125 

TABLE  9. 

Average  weight  per  cubic  foot  for  materials  used  in  the  con- 
struction and  loading  of  buildings. 


Woods. 


POtTNDS. 

Apple  tree 49 

Ash 52 

Beech 43 

Birch  (American) 40 

Butternut  ovhite  walnut) 23 

Cedar— red 40 

Cedar— Canadian 56 

Cherry 44 

Chestnut 41 

Cypress 27 

Dogwood 47 

Ebony  79 

Elm 36 

Fir  (Norway  spruce) 33 

Blue  gum 52 

Hemlock 26 

Hickory 58 


POUNDS. 

Larch 33 

Lignum  vitee 83 

Locust 46 

Mahogany  (Honduras) 40 

Mahogany  (Saa  Domingo) 50 

Maple 49 

Oak,  white 50 

Oak,  live 59 

Poplar,  or  white  wood 24 

Pine,  Georgia 48 

Pine,  white 28 

Rosewood 45 

Red  wood 23 

Spruce 30 

Walnut,  black 33 

Sycamore 37 


Metals. 


POUNDS. 

Brass  cast 525 

Copper  cast 5.55 

Cast  iron 450 

Gold  (standard) 1108 

Lead 712 


POUNDS. 

Silver  (standard) 644 

Steel 490 

Tin  cast 459 

Wrought  iron 485 

Zinc  cast 450 


'.:U 


MECHAXTf'AT.   nAlIPKXxnV. 


Stones. 


POUNDS. 

Alabaster 173 

Asphalt 150 

Asphaltum. 87 

Bricks,  pressed IM 

Bricks  conirnon  hard i'l'y 

Bricks,  soft KtO 

Brick  work,  press. 140 

Brick  work,  ordinary 113 

CeiiienI,  Portland Si 

Cement,  Rosendale 5(5 

Coal,  anthracite,  solid 93 

Coat,  anthracite, hroken  loose    CA 

Coal,  bituminous,  solid S4 

Ooal,  broken  loose 49 

Earth  loose    7t) 

Earth  rMunied 95 

Earth,  with  gravel 126 

Glass,  coimnon  window 157 

Gla.ss,  plate 172 


POUNDS. 

Gianite 170 

Glass,  flint 192 

Gypsum 143 

Lime,  quick .53 

Lime,  stone 1B9 

Lime,  stone,  broken  loose 96 

Marble 170 

Masonry.granite  or  limestone  165 

Masonry  of  ruble. 140 

M  asonry  of  sandstone.dressed  144 

Mortar,  hardened 103 

Porphyry. 180 

Quartz 165 

Rotten  stone 124 

Sand,  coai'se 112 

Sand,  moist 130 

Slate,  American 175 

Tile^ „.. „ „. 115 


Misc  ellan  eous. 


POUND.S 

Ashes,  wood. .    58 

Bark,  Peruvian 49 

Butter 59 

Coke 27 

Camphor 62 

Charcoal 26 

Cotton,  baled 20 

Pat 58 

Gunpowder 57 

Gneiss,  common 168 

Hay,  baled 17 

Ice 58 

Ivory 114 

Plaster  of  paris 73 

Petroleum 55 

Platinum 1342 

lied  lead. 559 

Rosin 69 

Salt,  coarse 45 

Salt,  wet 140 


iPcnrNDs- 

J?nOW,  jTIsTfalleb 5  to  12 

Snow,  moistened  by  rain.  .15  to  50 

Sulphur 125 

Saltpeter 131 

Tar 63 

Water,  rain  at  60°  F 62'2 

Water,  sea (U 

Wax,  bees 60 

Whale  bone 81 

Mercury  at32°F 849 

Mud,  wet  fluid 120 

Mud,  dry  compact 110 

Talc 156 

Soap _ _ _ 56 

Sugar 100 

Honev 90 

Milk.'. 64 

Fire  brick 137 

Clay. 125 


TABLE  10. 

Weight  per  Lineal  Foot  of  Square  and  Round  Iron. 

■Fry.] 


.Thickness 

Squai-e 

Bound 

Thickness 

Square 

Round  I 

or 

Bar  in 

in 

or 

Bar  in 

in 

Diameter. 

Pounds. 

Pounds. 

Diameter. 

Pounds 

Pounds. 

h 

0.0132 

0.0104 

H 

3.5790 

2.03.50 

4 

0.0.526 

0  0414 

1 

3.3680 

3.6450 

A 

0.1184 

0.0930 

IH 

5.3630 

4.1330 

1 

0.3105 

0.1653 

IK 

7.578 

5.953 

i"s 

0.3390 

0.2583 

IM 

10.310 

8.101 

a 

0,4736 

0.3730 

2 

13.470 

10..580 

.7_ 

0.6446 

0.5063 

Wa 

17.050 

13.S90   . 

i 

0.8420 

0.6613 

3K 

31.050 

16.530 

I 

1.8160 

1.0330 

2% 

35  470 

30.010 

3 

4 

1 .8950 

1.4880 

3 

30.310 

23.810 

-^  To  find  the  weight  of  a  scjuare  bar  H'^  thlck.and  1)4'^  wide  and 
"i''  long  from  the  above  table,  take  the  decimal  .3105.  opposite  %,  and 
multiply  by  6.  or  take  one-sixth  of  tlie  sum  opposite  1)4  (7.578) 
for  the  weight  of  a  foot  lineal;  thus,  7.578^6—1.263  pounds. 


Mechanicat,  Carpe??tuy. 


fSS 


TABLE  11. 

To  Find  the  Weight  of  Castings  from  their  Patterns. 

Multiply  weight  of  white  pine  pattern  by  16  for  cast  iron. 

"  "  "        "  "  '•  18    "  bi'ass. 

"  "  "        "  "  "  19    "  copper. 

"  "  25    "  lead. 


TABLE  12. 
The  Weight  of  Various  Metai>s  Per  Superficiat,  Foot. 

[Fry.] 


Thicivness 
in    trac- 
tions of 
an  Inch. 

g 

M 

O 

tr. 

a 
o 

•6 

Hi 

6 

a 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

_)L 

2.344 

2.526 

2.. 552 

2.734 

2.891 

3.708 

2.344 

k 

4.687 

5.0.'52 

5.104 

5.469 

5.781 

7.417 

4.687 

A 

7.031 

7.578 

7.656 

8.203 

8.672 

11.125 

7.031 

\ 

9.37.'5 

10-104 

10.208 

10.938 

11.. 563 

14.833 

9.375 

^6 

11.719 

13.630 

13.760 

13.673 

14.453 

18.540 

11.719 

I 

14.063 

15.156 

15.312 

16.406 

17.344 

23.250 

14.063 

/e- 

16.406 

17.683 

17.865 

19.141 

20.234 

25.9.58 

16.406 

1 

18.750 

20.208 

-20.417 

21.875 

23.125 

29.667 

18.7.50 

^ 

28125 

30-312 

30.6-25 

33.813 

34.688 

44.500 

28.1-35 

1 

37.. 500 

40.417 

40.833 

43.750 

46.2.50 

59.333 

37.500 

TABLE  13. 

Weight   per   Superficial  Foot   on  Roofs  from  Various 
Causes. — [Thurston.] 

LBS. 

Weight  of  >§'  slating  on  1  inch  sheathing 6.75 

of  {>g  slating  on  1  inch  sheathing 9.00 

of  1^  slating  on  1  inch  sheathing 11.25 

if  slate-felt  be  used,  add 25 

or  laid  in  mortar,  add 3.00 

of  snow  on  roof '30.00 

from  wind  pressure — [Trautwine] 40.00 

for  roofs  not  over  seventy-five  foot  span. 

W^eight,  if  covered  with  corrugated  iron,  unboarded 28.00 

"      if  plastered  below  the  rafters 38.00 

if  corrugated  iron  on  sheathing  boards 31.00 

if  plastered  below  the  rafters 41.00 

if  slated  on  laths 33.00 

if  slated  on  1^  inch  boards 35.00 

"      if  plastered  below  the  rafters 46.00 

"      if  shingled  on  lath 30.00 

"      if  plastered  below  the  tie  beam ...  40.00 

"      if  roof  be  from  75  to  100  foot  span  add  to  each 4.00 


5J36  Miscellaneous. 


Excavators'  Memoranda. 


Exca/atlng  is  computed  by  the  cubic  yard  of  27  cubic  feet; 
aud  paving  by  the  superficial  yard  of  9  square  feet. 

To  ascertain  the  numl>er  of  cubic  yards,  multiply  the  length 
by  the  breadth,  aud  that  sum  by  the  deptli,  ail  in  feet;  then  divide 
by  27.  If  to  find  the  number  of  bushels,  divide  by  2,150.42;  or 
to  find  the  number  of  gallous-  divide  by  231. 

If  the  plot  to  be  excavated  is  uneven,  aud  apt  to  lead  to  dis- 
putes after  being  excavated;  then  survey  the  portion  to  be  dug  out, 
with  a  Comstock  level,  by  taking  levels  at  regular  intervals  over 
the  surface,  and  from  the  average  calculate  the  amount  of  earth 
to  be  removed,  before  commencing  the  work. 

To  take  tha  levels,  locate  the  instrument  at  the  highest  point, 
say  four  feet  above  the  earth  surface.  Now  the  level  of  founda- 
tion below  the  earth  surface  at  the  high  point  is  10'';  then  take 
levels  at  intervals  over  the  plot  to  be  excavated  from  the  level  of 
instrument  to  the  earth  surface,  and  deduct  the  perpendicular 
heights  from  the  10''.  Now  suppose  levels  at  regular  intervals 
for  25  points  have  been  taken,  and  the  remainders  summed  up  and 
divided  by  25  will  give  the  average  depth  of  excavation  or  earth 
to  be  removed, 

TABLE  14. 


Clean  dry  Sand  aud  Oravcl  in  excavation,  will   retain  a  ver- 
tical face  of  one  foot  for  a  short  time  without 

caving  in =  0  to  1  foot. 

Moist  Sand  and  ordinary  Surface  Mould =  1  to    3  feet. 

Loamy  Soil,  well  drained, =  5  to  10     " 

Clay, =  9  to  13     " 

Compact  Ch-avel  Soil,  for  a  short  time.. =10  to  15     " 

Hurst. 
A  cubic  yard  of  earth,  when  dug  up,  will  occupy  from  1  ^^  to 
1)4  cubic  yards. 

Paving  Brick  should  measure  9''''X4K'"X1^''''.  and  weigh 
from  4  to  4K  pounds  each.  One  yard  of  paving  requires  32  paving 
brick,  laid  flat,  and  83  on  edge. 

14  cubic  feet  of  Chalk  weighs  1  Ton, 

18  "        "         Clay  "      1     " 
31      ''         ••          Earth         '•       1      " 

19  ••         •'  Gravel       "       1      '• 
22      "         ••          Sand  ••       1     " 


MlSCELI-AXEOXTO. 

TABLE  15. 


SST? 


Number  of  Cubic  Feet  to  be  Eemoved,  axd  the  Number  of 
Bkick  Eequiked  fok  Wells  from  3'  0''  to  12'  0''  nf 
Diameter. 


O  d) 

1  i 

fSfo 

0  a 

a 

o«  be 
6^S 

.2g 

-^2 
62.2 

0  03  ® 

0  a.= 

So  h 

0 

^5f 
0  a.a 

o 

JC    *" 

^ 

"Z 

0 

z 

» 

;2: 

3'  0^' 

,••2 

11.0446 

66 

7/6// 

1 

63.6174 

347 

3^6^' 

>3 

14.1862 

77 

8^0^' 

70.8823 

368 

4/0/' 

J^ 

17.7205 

88 

8' 6^' 

78.54 

390 

4' 6'' 

K 

21.6475 

99 

9'0^' 

86,5903 

413 

5'0'' 

H 

25.9673 

110 

10'  0'' 

103.8691 

457 

5' 6'' 

K 

30.6796 

121 

10' 6^' 

113.0976 

479 

6'0'' 

K 

35.7847 

132 

11'  0" 

123.7187 

500 

6' 6'' 

1 

50.2656 

302 

11'  6" 

132.7326 

523 

-/()// 

1 

56.7451 

3-24 

12'  0" 

143.1391 

546 

Stonemasons'  Memoranda. 


Cellar  walls  should  be  constructed  of  stoue,  carried  up  above 
the  ^ound.  Brick  should  not  be  used  for  outside  cellar  walls,  as 
the  dampness  will  rise  by  capillary  attraction  injurhig  the  joist 
and  render  the  rooms  unhealthy;  this  may  be  obviated  by  providing 
a  damp  course  of  slate  and  pitch  under  the  first  floor  of  joist. 

FoGtiirgs.  The  New  York  City  Building  Laws  require  them 
13"  wider  than  the  thickness  of  wall  next  above  them,  and  IS" 
projection  aroiuid  all  foundations  for  piers,  colurans,  posts  or  pil- 
lars, and  18"  in  thickness,  and  all  laid  in  cement  mortar. 

Stoue  foundations  shall  be  at  least  8"  thicker  than  the  wall 
next  above,  to  a  depth  of  16  feet  below  the  curb  level,  and  shall 
be  increased  4"  in  thickness  for  every  additional  five  feet  the  wall 
is  deeper.  All  fouudation  walls,  either  of  brick  or  stone,  are  re- 
quired to  be  built  in  cement  mortar,  for  ali  high  buildings.  For 
ordinary  dwelling  houses  of  two  or  three  stories,  the  basement 
walls  are  usually  of  common  ruble  18"  thick,  built  in  commoa 
mortar,  and  having  a  footing  course  of  heavy  stone  projecting  6" 
on  each  side  whenever  practicable. 

For  high  and  massive  buildings  in  the  city  of  Chicago,  owing 
to  the  yielding  nature  of  the  soil,  the  entire  excavation  is  some- 
times covered  over  with  rail  road  iron,  bedded  in  concrete;  then  the 
foundation  walls  are  started  otf  the  concrete. 

Where  the  soil  is  compressible,  piling  is  resorted  to  as  a  base 
for  foundation  walls;  wooden  piles  should  not  be  used  iu  dry- 
soils,  but  in  water  they  have  proved  to  be  durable;  they  are 
usually  20  to  35  feet  loog,  owing  to  the  depth  required  for  a  solid 
base. 


238  MiSCELLAXEOrS. 

Load  on  piles.  When  a  wooden  pile  refuses  to  sink  over 
)4  inch  under  a  blow  from  a  ram,  weighing  2,500  lbs.,  falling 
30  feet,  it  is  considered  home.  Brevet  Major  John  Sanders,  U. 
S.  Engineer,  gives  a  formula  for  a  safe  load,  thus  : 

=Safe load. 


8 

R  equals  the  weight  of  ram  in  pounds. 

h  equals  the  height  of  fall  in  inches. 

d  equals  the  distance  the  pile  sinks  from  the  last  blow  in 
inches. 

Example.     Required  the  safe  load  of  a  pile,  the  ram  weigh- 
ing 1,200  pounds,  dropping  6  feet  and  driving  the  pile  3  inches. 
1,200X72-^8 
^ =3,600  pounds  as  the  safe  load;  if  the  pile  refused  to 

sink  over  }i''  under  the  above  conditions,  then  the  safe  load 
would  be  43,200  pounds. 

For  the  crushing  strength  of  stones  and  mortars,  the  student 
is  referred  to  Tables  7  and  8. 

Ruble  masonry  is  valued  by  the  perch,  containing  24%  "ubic 
feet.  To  lay  a  perch  of  ruble  masonry,  it  requires  about  3  bushels 
of  sand  and  1  bushel  of  lime;  for  good  ruble  work,  the  stone  on 
the  corners  and  jambs  should  be  lapped,  and  through  stones  every 
five  superfical  feet  in  all  straight  walls,  and  no  stones  built  in  on 
edge,  but  on  their  natural  bed.  The  proportion  for  mortar  is  3 
bushels  of  sand  to  1  of  lime.  Concrete  is  made  by  mixing  gravel, 
broken  stone,  brick  or  slag,  with  1  part  of  cement,  6  parts  of  clean 
sautl  and  other  solid  components,  and  \}4  parts  of  water;  and 
thorouglUy  mixed  and  carefully  rammed  in  place;  and  is  measured 
by  the  actual  contents. 

MeuHunivj  Stonework.  Girt  around  the  building,  adding 
twice  the  thickness  of  walls  at  the  internal  angles,  including  all 
openings  that  are  not  over  4  feet  wide,  in  walls  under  two  feet 
thick;  also  including  all  openings  five  feet  wide,  when  the  walk-; 
rae  two  feet  to  2'  6"  in  thickness.  When  the  openings  are  over  5 
feet  wide,  add  one  thickness  of  wall  to  the  width  of  each  jamb 
only. 

Footings  measured  same  as  main  wall.  All  arches  to  be  girt 
and  one-half.  All  safety  arches  to  be  considered  extra.  All 
abutments  that  project  out  from  the  wall  six  inches  and  under  to 
have  12  inches  added  on  each  end.  All  abutments  abo^e  6  inches, 
aud  not  over  18  inches,  to  be  girt  measure  only. 

All  piers  that  are  built  by  themselves,  and  are  3  feet  square 
and  under,  to  be  girt  and  one-half  by  one  foot  thick;  aud  all  pier- 
that  are  three  feet  square  and  upward,  to  be  ftieasured  solid,  with 
9  feet  added  for  each  foot  in  height  for  corners.  Circular  walls 
to  l>e  girt  and  one-half. 

Recesses  and  slots  to  be  measured  solid.  No  reductions  made 
for  cut  stone  trimmings  and  lintels.  Quarry  measure  in  all  cases 
to  be  solid. 

Cut  Stone  Setting.  Measure  vault  covers,  flagging  and  ashler 
by  the  superficial  foot.  Coping  aud  belt  courses  by  the  lineal 
foot;  all  other  cut  stone  by  the  cubic  foot. — Hand  Book  of  the 
Pittsbinyh  Builders'  Exchawje. 

':    ■     For  the  number  of  brick  per  superficial  foot  in  a  wall,  add 
seven  brick  for  everv  half  brick  the  wall  is  thick. 


MlftCELLAXEOtTS.  239 


BncKiayers'  Memoranda. 


TABLE  16. 


Nv-ifBEn  OF  Hai,k  Bkicks  in  the  Thickne.«5s  of  Wall  per 
St'pekficial  foot  of  avall  surface. 


1 

0 

3 
21 

4    j      5           6 
28        35        42 

7 

fi 

No.  of  brick  per  super- 
ficial feet 

7 

14 

49 

56 

Example  :  Required  the  number  of  brick  in  a  wall  40  feet 
long,  25  feet  high  and  4  half  brick  in  thickness.  Under  4  in  the 
above  table  is  28  brick  to  the  superficial  foot. 

Then  40X-25X-38=28,000;  equals  28,000  brick. 

The  size  and  quality  of  brick  vary  in  different  localities. 
The  standard  size  in  Western  Pennsylvania  is  8>.2^4J^X2^  thick, 
and  weight  5  to  6  pounds  each,  and  for  a  good  quality  they  should 
not  absorb  over  one-twentieth  their  weight  of  water  when  dry. 

A  bricklayer's  hod  measures  9^'X9'^X16"  long,  and  holds  16 
brick;  the  Y  angle  should  be  60  degrees.  Ladder  rungs  should 
not  be  over  9^''  from  centers;  1000  brick  closely  stacked  occupy 
about  .56  cubic  feet;  1000  old  brick  cleaned  and  loosely  stacked 
occupy  about  72  cubic  feet;  1000  brick  require  about  '6^i  bushels 
of  lime  and  9  bushels  sharp  sand. 

A  load  of  mortar  measures  1  cubic  yard,  or  27  cubic  feet;  a 
double  load  measures  twice  the  above  quantity. 

Strength  of  Brick  Work.  Mr.  Trautwine,  Civil  Eugi- 
neer.  states  ordinary  brick  work  cracks  wilh  20  to  30  tons  pres- 
Bure  per  square  foot,  or  311  to  466  pounds  per  square  iucli,  and 
for  good  brick  work  in  cement,  770  to  1088  pounds  per  square 
inch. 

The  New  York  City  building  laws  require  that  brick  cellar  walls 
shall  be  four  inches  thicker  than  the  walls  next  above,  and  the  in- 
crease below  the  curb  level  is  the  same  as  for  stone  foundations, 
which  see  :  For  buildings  not  over  55  feet  high,  external  walls. 
13'''  thick;  exceeding  55  feet  and  not  over  80  feet,  \&'^  to  top  of 
jirst  story,  thence  if  not  over  40  feet  to  be  12"  thick;  more  than 
80  feet  then  4^'  to  be  added  for  every  15  feet  the  building  is  higher 
tlian  80  feet.  If  brick  be  used  for  foundation  walls,  they  must  be 
laid  in  cement  for  all  large  buildings. 

'  Mr.  F.  E.  Kidder,  March  :30ll),  1882.  at  the  U.  S,  Arsenal  in 
Watertown,  Mass.,  made  some  experimental  tests  on  brick  piers, 
for  the  purpose  of  comparing  different  kinds  of  cements  with 
common  mortar  and  sand.  The  common  mortar  was  taken  from 
a  building  in  course  of  erection  near  by.  Seven  ditferent  tests 
are  shown  in  Table  17.  The  Portland  cement  used  in  the  build- 
ing of  these  piers  is  known  as  Brooks,  Shoobridge  &  Co.'s  cement. 


240 


MlSCKI^LAKEOrS. 


•>108J0  %e.i]g^ 


•sajnuua 
n]lS8^  JO  a  rat  X 


•Si^'Bp  92  'sqinotn  f 

:aSV 


•spunod  u{  4q§ie^v^ 


S       8 
8       8 


o         «s 


•asjnoo  JO  q^Suai       a 


■//2lX,/8  Jaid  JO  9zts 


oj  paonamraoo  .i9ia  oj  n? 
aqi  qoiDAV  jopun  5  '  ^ 
ui  'bs  .led  a.mssyj({        | 


3    S 


•jaid  JO  tri 


S    S 


t- « 


9  -^ 

CO  Ha-  I 
•3   ;3 

6     6 


^ 

il9 

■c 

:  s-i 

c 

:  rt 

r* 

•  ;-.^ 

■  c 

;_ 

-» 

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3  O 

C 

-c 

^ 

0)  cj  ■"> 

3S- 
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■^  i  a:  +i  c3  *^  K 

^  c  c  «  c  ®   ■ 

:        s:  CS  r;  «*  ^ 


o     o 

55  ^ 


TABLE  18. 
Table  Showing  the  Thickness  of  Walls  for  Dwellings 
AND  Stores,  as  Set  Forth  in  the  Building  Laws  of 
THE  City  of  Chicago. 


Basement  and  two  stories 

Basement  and  three  stories 

Division  walls,  basement  and  two  stories 

Moi'e  than  three  stories 

Division    walls,    basement    and    three 

stories 

Division     walls,    basement     and     four 

stories 

When  fli'st  story,  or  basement  and  first 
story,  are  for  shop  or  stores,  then: 

Two  stories  and  liasement 

Three  stories  and  basement. 

Four  stories  and  basement 

Three-story  building,  division  wall 

Four-storj'  building,  division  wall 


12" 
15" 
12'/ 
16" 

12" 

16" 


12" 
16" 

2(V' 
12" 
16" 


8" 
12" 

8" 
16" 

12" 

12" 


12" 
16" 
16" 
12" 
16" 


12" 

8" 

li" 


12" 
12" 
12" 

12" 


12" 
1?" 


Miscp:lla>'eous.  g^l 


Plasterers'  Memoranda. 


TABLE  19. 

MATEKIAL  BEQUIEED  for    100    YAKDS    OF    PLASTEIJING,  THltEE 
COATS   COMMON. 

Lime, 12  buslieis. 

Sand, 36        " 

llair, 2        " 

8  d  Nails  (fiae)  for  joist  spaced  2'  C'  from  centers,    6>^  pounds. 
3d      "        "            "            "      V  A^'     "          "         8K         " 
3d      "         "            "            "      1^0^^     "          "        10>^        " 
Number  of  lath  required, 1,600. 


Latlis  are  cut  4^  0'^  by  \%^^  by  %^^  standard. 

One  bushel  of  hair  equals  8  pounds  standard. 

One  yard  of  plastering,  three  coat  work,  requires  nearly  one- 
half  peck  of  uuslacked  lime,  and  nearly  a  peck  and  a  half  of  sand, 
and  16  lath. 

One  load  of  mortar  or  sand  meaures  one  cubic  yard,  and  will 
fill  21  hods. 

A  plasterer's  hod  measures  IS*"  by  15''  by  33''  long,  the  V 
is  60  degrees,  and  contains  a  bushel  of  mortar. 

Plain  plastering  is  valued  by  the  yard,  of  9  square  feet;  when 
the  material  is  furnished  by  the  plasterer,  deduct  the  half  of  all 
openings  over  9  square  feet,  and  add  all  openings  that  are  9  square 
feet  and  under;  deduct  all  openings  measuring  100  square  feet 
and  over. 

When  materials  are  not  furnished  by  the  plasterer,  no  deduc- 
tions for  openings  are  made. 

All  cupboards,  closets,  pantries,  and  all  circular  work,  are 
measured  double  full  height  to  the  ceiling;  Softils  of  staircases  are 
measured  one  and  a  half  times.  All  arrises,  quirks  and  cham- 
fered corners  are  measured  by  the  lineal  foot,  yiucco  cornice  is 
measured  by  the  square  foot.  Oirt  around  all  members,  and  add 
one  foot  lineal  for  every  miter  for  the  length,  by  (lie  girt;  any  cor- 
nice or  moulding  less  than  12"  girt,  shall  be  measured  as  12"  girt. 
Ellipsis  are  measured  three  times.  For  eurichmeuts,  charge  by 
the  piece. 


12 


243 


Miscellaneous. 


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Miscellaneous. 


243 


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244 


Miscellaneous. 


TABu^E  21. 


Number  of  Shingles  and  Nails  tek  100  Squaue  Feet. 


Laid  to  the 

Nurnhcr  per  100 

weather. 

sq 

uiire  feet. 

4// 

1,000 

41^// 

890 

5" 

800 

5H^' 

727 

(S" 

667 

Kuiiibei-  of 
5  d  nails. 


5 

4>^ 
4 

3^ 
3K 


TABLE  22. 


The  standard  width  of  shingles  is  4^^. 

1000  feet  of  sheathing  on  rafters  spaced  2'  d"  from  centers 
requires  29  lbs.  lOd  nails. 

1000  feet  of  sheathing  on  rafters  spaced  I'C'^  from  centers 
requires  40  lbs.  lOd  nails. 

1000  feet  of  sheathing  on  rafters  spaced  1^4^'  from  centers 
requires  45  lbs.  lOd  nails. 

1000  feet  of  sheathing  on  rafters  spaced  \'  ^"  from  centers 
requires  GO  lbs.  lOd  nails. 

1000  feet  llooring  joist  spaced  \'  ^"  from  centers  requires  40 
lbs.  8d  nails. 

1000  feet  ^"  weather  boarding  studding  spaced  1'  ^"  from 
centers  requires  3.")>2  lbs.  8d  nails. 

1000  feet  lath  on  studding  spaced  V  \"  from  centers  requires 
5  %  lbs.  od  tine. 

For  flooring  and  weather  boarding  allow  one-fifth  for  waste 
and  matching. 


MiSCELLAKEOtrS. 


^. 


TABLE  23. 


Approximate  number  of  cut  axd  wire  xails  to  the  pound. 


Leugtli 

in 
inches 

Cut 
nails 

Wire 

finisli- 

ing 

Wire 
fence 
nails 

Wire 
slating 

Wire 

roofing 

Wire 
com- 
mon 

2(1 

1 

1,558 

411 

411 

1,200 

3d  fine. 

1% 

760 

3d 

IH 

480 

980 

329 

251 

720 

4d 

iVi 

300 

760 

209 

165 

432 

5d 

1% 

2G0 

500 

142 

142 

142 

300 

6d 

2 

160 

350 

124 

103 

252 

7d 

2H 

128 

275 

92 

ISO 

8d 

2X 

92 

190 

82 

132 

9d 

3M 

72 

173 

62 

105 

lOd 

3 

60 

137 

50 

87 

12d 

^H 

44 

98 

38 

66 

Itid 

3K 

32 

81 

30 

51 

sod 

4 

24 

71 

23 

35 

30d 

iH 

18 

27 

40d 

5 

14 

21 

.50d 

5K 

12 

15 

God 

6 

10 

12 

6d  ^^'If'' 
nails. 

2 

80 

8d      " 

2}i 

50 

lOd      " 

3 

39 

IM      " 

314 

24 

Speeding  Pulleys.  Tlie  diameter  in  inches  and  number 
of  revolutions  of  the  driver  helng  given,  required  the  number 
of  revolutions  of  tl\c  driven. 

Rule.  Multiply  the  diameter  of  the  driver  in  inches  by  its 
number  of  revolutions,  and  divide  by  the  diameter  of  the  driven 
in  inclies,  for  its  number  of  revolutions. 

The  dkancter  in  inches  and  number  of  revolutions  of  the 
f7ru'C/i  helncj  given,  required  the  diameter  of  the  driver  for  a 
given  nuraber  of  revolutions. 

Rule.  Multiply  the  diamever  of  the  driven  in  inches  by  its 
number  of  revolutions,  and  divide  by  tlie  given  number  of  revo- 
lutions, for  the  diameter  of  the  driven  required  in  inches. 

The  diameter  in  Indies  and  number  of  revolutions  of  tlie 
driven  being  given,  required  the  diameter  of  tlie  drivendn  inches. 

Rule.  Multiply  the  diameter  of  the  driven  in  inches  by  its 
number  of  revolutions,  and  divide  by  the  number  of  revolutions 
of  driver  for  its  diameter  iu  inches. 

Pulleys.  Are  of  two  Icinds,  "straight  face  "  for  shifting 
belt,  and  "crown  face "  for  non-shifting. 

Belting.  To  give  durability  to  fast  running  belts,  grease 
them  well  with  castor  oil. 


'246  MiSCEttAiTEOtTS. 

When  endless  belts  can  be  used  splice  them  about  ^",  glue 
and  clamp,  let  stand  over  niglit,  then  peg  with  wooden  pegs  set 
in  glne.     This  is  better  by  far  than  leather  lacing. 

The  best  lacing  for  belts  in  last  speed  is  annealed  brass  wire 
of  No.  55  gauge  for  narrow  belts. 

Weight  of  Grindstone.  Rule.  Square  the  diameter  in 
inches  and  multiply  by  the  thickness  in  inches,  and  that  sum  again 
by  the  decimal  0.06363.  for  the  number  of  pounds. 

To  find  tJie  pressure  per  sqiiare  inch  of  water  in  a  Umh  10' 
square  and  W  deep. 

A  cubic  foot  of  water  at  a  temperature  of  60  degi-ees  F. 
weighs  62 K  pounds,  or  8.3  pounds  to  the  gallon;  at  213  degrees 
weight  is  59.80,  or  8.3  pounds  per  gallon.  The  pressure  per 
square  inch  of  a  column  of  water  one  foot  high  equals  0.434 
pounds;  hence  a  column  of  water  12  inches  square  and  10  feet 
high  at  a  temperature  of  60  degrees  will  exert  a  pressure  on  the 
bottom  of  tank  equal  (10X62^=625  lbs.)  to  625  poinids,  or  equal 
(625-^-144=4.34)  to  4.34  pounds  per  square  inch  nearly;  then 
120^^X130^^X4.34=62.496,  equals  6,i,496  pounds  as  the  pressure 
on  the  bottom  of  the  tank.  The  pressure  on  the  sides  of  tank 
diminishes  as  the  height  decreases;  at  the  top  the  pressure  is 
nothing,  while  at  the  bottom  the  pressure  per  square  inch  is  equal 
to  the  height  (10')  in  feet  multiplied  by  4.34;  hence  the  average 
pi-essure  on  one  side  of  the  tank  will  equal  one-half  4..34  (3.17) 
multiplied  by  its  area  in  inches;  thus,  120X130X2.17=31248; 
equals  31,248  pounds  on  one  side  of  the  tank. 

Ohie.  The  cohesion  of  solid  glue,  Mr.  Bevaii  found  to  be 
4,000  pounds  per  square  inch;  his  experiments  on  pieces  of  wood 
glned  together,  req^uired  a  force  per  square  inch,  of  350  to  715 
pounds  to  separate  them. 

Good  glue  is  very  hard  and  tough,  and  of  a  brown  color;  is 
transparent  if  held  to  the  light,  the  fracture  is  ragged  and  oblique 
to  the  edge,  is  almost  tasteless,  and  no  bad  smell,  swells  when 
soaked  in  cold  water,  requires  to  be  boiled  before  it  will  thoroughly 
dissolve,  requires  about  t«n  times  its  w-eight  of  water;  it  also 
forms  a  stiff  jelly  when  cold,  which  is  a  fair  test  for  good  glue. 

Poor  glue  is  dark  and  cloudy,  breaks  easy,  having  a  straight 
or  conchoidal  fracture  and  glass  edge,  is  easily  dissolved  in  cold 
water;  if  exposed  to  dampness,  will  emit  a  bad  smell  in  a  short 
time. 

To  prepare  tlie  glue.  Place  the  amount  of  glue  to  be  used,  in 
a  bag  of  some  strong  material,  then  pound  with  a  mallet;  place 
the  glue  in  tiie  pot,  cover  with  clean  cold  water,  let  stand  over 
night;  then  place  the  pot  in  the  kettle  filled  with  water,  let  boil, 
and  stir  well,  remove  the  scum,  and  when  the  glue  will  run  from 
the  brush,  smooth  and  free,  having  no  lumps,  is  ready  for  use. 
Apply  hot,  the  hotter  the  glue  is  the  better  will  be  the  joint.  In 
cold  weather,  warm  the  joints  to  be  glued,  but  not  too  hot  to  burn 
tlie  glue;  after  applying  the  glue,  rub  the  joint  well,  to  lessen  the 
film  of  glue  in  the  joint,  and  thus  form  a  grain  and  suction  in  the 
joint:  the  work  may  now  be  clamped  and  let  stand  until  dry, 
which  for  heavy  work  will  require  from  two  to  three  days,  for 
light  work  less  time  will  suffice;  if  the  glue  is  a  little  thick,  only 
apply  it  to  one  side  of  the  joint.  A  spoonful  of  whitening  to  a  pot 
of  glue  is  said  to  improve  the  strength  of  same;  a  little  alcohol  will 
keep  the  glue  sweet;  fresh  glue  is  always  the  best.  When  re- 
melted  its  strength  decreases,  and  if  burnt  it  is  worthless.  Clean 
boiling  water  should  be  used  to  thin  down  if  too  thick;  the  pot 
should  be  thoroughly  cleansed  when  making  fresh  glue,  as  the  old 


MlSCKI.T.  ANEOUS . 


247 


will  taint  and  ruin  the  new.  When  not  in  use,  place  the  pot  in  a 
cool  place  apart  from  the  kettle;  if  a  cover  be  placed  over  the  pot, 
the  moisture  will  keep  the  glue  from  crisping  on  the  sides. 

2'uiiiers'  Cement.  To  one  pound  of  melted  rosin,  add  a  quar- 
ter pound  of  pitch;  whilo  boilins:,  add  brick  dust  until  considered 
thick  enough,  roll  into  sticks  same  as  grafting  wax.  When  turn- 
ing rosettes  or  other  light  work,  by  heating  the  above  cement  the 
work  may  be  attached  to  the  face-plate,  and  removed  with  a  light 
tap  from  the  hammer;  in  winter  add  a  little  tallow. 


Glossary  of  Technical  Terms 

—  AND  — 

GENERAL  INDEX. 


Aaron's  Rod. — An  enrichment 
consisting  of  a  straight  rod  from 
■which  almond  leaves  are  repre- 
sented sprouting  on  each  side; 
the  term  has  been  applied  incor- 
rectly to  a  rod  around  which  a 
serpent  is  coiled. — [Audsley. 

Abacas.  —  The  upper  number  in 
the  capital  of  a  column,  on  which 
the  architrave  in  classic  and  the 
springers  in  Gothic  architecture 
immediately  rest;  in  the  Tuscan, 
Doric  and  Ionic  orders  it  is  rec- 
tangular; in  the  Corinthian  and 
Composite  orders  the  abacus  is 
curved  outward  at  the  angles 
termed  the  horns;  the  curve  is 
ornamented  at  the  center  with  a 
rosette,  termed  the  rose  of  the 
abacus. 

Abntment.  —  A  construction  of 
stone,  brick  or  other  material 
which  receives  the  thrust  of  an 
arch,  vault  or  strut. 

Acroferia.  —  A  small  pedestal 
placed  on  the  apex  or  angles  of  a 
pedement  for  the  support  of  a 
statue  or  other  ornament. 

Acute  Angle.— Page  21. 

Albarnom.- Sap  -wood. 

Alcove.— A  recess  in  a  room  for  a 
bed,  sometimes  curtained  oiT  and 
Jiid  from  view  during  the  day. 

AJJar-ISail.— The  railing  of  stone, 
marble,  metal  or  wood  in  front  of 
the  communion  table,  and  in 
front  of  which  communicants 
kneel  while  receiving  the  sacra- 
ment; the  height  from  the  top  of 
kneeling  step  is  about  2'  2". 

Algebraic  Symbols.— 230. 

Asiijle-Bracket— A  bracket  placed 
in  an  interior  or  exterior  anple, 
and  not  at  right  angles  with  the 
wall;  to  fuid  the  length  and 
curve.    222,  223. 

Ajuglc-tie.— The  timber  that  gives 
support  to  the  clragon-hcam  in  a 
roof;  the  diagonal  piece  cut  in 
the  anjjlcsof  a  square  frame  to 
redvxco  the  same  to  an  octagon. 

AMglc-Bea<!.— Or  soTiictimes  term- 
ed staff  head,  is  used  as  a  saddle 
on  the  external  angles  of  plas- 
tered walls  to  protect  them  from 
injury;  if  a  column,  it  is  termed 
an  anijlc  column;  if  a  corbel,  it  is 
tci'med  an  anale  corbel. 

Angnlar-fapital.  —  In  the  Ionic 
capital  wiiere  the  three  volutes 
are  made  to  the  angle  of  135  de- 
grees from  all  four  sidles. 

Anuiilct. — A  small  fillet  circular 
on  plan,  and  square  in  section. 

Antique— In  architectural  nomen- 
clature, a  term  applied  to  works 
executed  by  the  ancient  Greeks 
and  Romans. 

Apron-piece.- The  cap  and  fascia 
completing  the  inside  finish  for 
the  window  sill,  and  on  whicli  the 
architrave,   or  moulding  finish 


around  the  window  sometimes 
rest;  is  also  termed  the  windom 
stool.  The  horizontal  piece  of 
timber  in  a  stair-case  for  sup- 
I  porting  the  rough  horses  at  plat- 
'  forms,  and  quarter  jjaces;  is  also 
termed  the  apron  piece.— [Nich- 
olson 

Arc  of  a  Circle.— In  geometry,  any 
part  of  the  circumference  of  a 
circle  that  is  less  than  a  semi- 
circle. 24.  Applied  to  transfer 
angle.  26. 

ArcSiitect.— Chief  of  the  works;  a 
person  competent  to  design  and 
superintend  the  execution  of  any 
building.  The  knowledge  he 
ought  to  possess  is  wide  and  va- 
variod,  comprehending  all  the 
trades  and  materials  in  the  con- 
struction of  buildings;  he  should 
be  kind  and  gentle  with  those 
who  are  calledupon  to  carry  out 
his  designs,  and  in  so  doing  ho 
should  be  positive  and  deter- 
mined to  checli  any  effort  to 
slight  or  deceive  in  the  work. 

Arch. — A  concave  structure  raised 
or  built  over  a  center,  and  serv- 
ing as  the  support  of  some  super- 
structure. When  several  arches 
are  built  in  a  row  it  is  termed  an 
arcade.  The  lino  from  v/hich  the 
arch  springs  is  termed  the  spring- 
ing line;  the  first  arch  stone  is 
termed  the  springer;  the  impost 
mouldinrj  is  the  cap  from  which 
the  arch  springs.  Tuearchstones 
are  termed  voussiors;  the  concave 
side  of  arch  is  termed  the  intra- 
dos,  the  opposite  or  convex  side  is 
termed  the  extrados;  the  solid 
extremities  on  or  against  which 
the  arch  rest  are  termed  tho  abut- 
ments; the  horizontal  distance  on 
the  concave  side  from  spring  to 
spring  of  the  arch  is  termed  the 
span. 

The  perpendicular  height  from 
springing  to  the  concave  side  at 
its  highest  point  is  termed  tho 
rise  of  arch;  tlio  croAvn  of  the 
arch  is  its  highest  point  on  tho 
intrados;  the  center  stone  at  t))u 
crown  is  called  the  keystone;  tlie 
haunches  of  an  arch  .arc  the  parts 
between  the  crown  and  tho 
sin'inging.  The  surface  of  tlie 
concave  side  is  termed  ihosofflt; 
and  when  a  collection  of  mould- 
ings is  carried  around  the  arcli 
concentric  with  tlie  intrados  tliis 
ornamentation  is  tcr;iied  tho 
archivolt;  and  the  mixed  right 
angle  triangle  formed  by  tbo 
curve  of  extrados  intersecting 
horizontal  and  perpendicular 
lines  draw  tangent  to  the  ex 
tradocs,  is  termed  tho  spandrel. 
The  spandrel  is  sometimes 
pierced  with  a  round  opening 
termed  an  o.rcyc.  Various  names 
arc  given  to  arches,  owing  to 
their  profile.    When  a  semi-cir- 


u 


GlooSakv  and  Index. 


cle  it  is  termed  a  circular  archi 
when  a  semi-ellipse  is  termed  an 
elliptical  arch ;  when  less  than  a 
semi-circle  it  is  termed  a  se^- 
mental  arch;  when  more  than  a 
semi-circle  it  is  termed  a  horse- 
shoe or  sarasenic  arch;  when  an 
arch  is  drawn  from  two  centers 
on  the  springing  line  it  is  termed 
a  pointed  arch,  or  Gothic  archi 
when  springing  from  imposts  at 
different  heights  it  is  termed  a 
rampant  arch ;  when  a  portion  of 
straight  exists  between  the  im- 
post moulding  and  the  springing 
of  the  arch  it  is  tei-med  a  stilted 
arch. 

Architrave.— The  band  or  finish 
carried  around  a  window  or  door, 
composed  of  one  or  more  mem- 
bers; also  one  of  the  three  divi- 
sions in  the  entablature  of  the 
classic  ordere.resting  immediate- 
ly on  the  abacus. 

Arcliivolt.— An  ornamental  band 
of  mouldings  concentric  with  the 
concave  side  and  worlced  on  the 
arch  stones,  and  terminating  at 
the  impost  moulding.  Sometimes 
the  keystone  divides  tlie  archi- 
volt  at  the  crown  of  arch. 

Area.— In  geometry  thesuperficiul 
contents  of  any  figure.  In  archi- 
tecture, an  open  space  allowed 
below  the  surface  of  ground  for 
basement  steps,  or  a  court. 

Arris. — The  external  angle  formed 
by. the  meeting  of  any  two  planes. 

Asiiicrin§^s. — Short  studding  cut 
under  ihe  rafters  in  the  garret  to 
cut  off  the  acute  angle  made  by 
the  rafters. 

Astraj^al.  —  A  small  projecting 
semi-circular  moulding;  it  is  also 
termed  a  bead,  ov  cockedhead,  and 
often  cut  Into  a  bead-mid  red  en- 
ricliment,  or  to  represent  a  string 
of  beads  or  berries. 

Atlantes.— Figures  of  males  used 
instead  of  columns  to  support  nn 
entablature;  if  females,  they  are 
termed  caryatidct<. 

Attic  Order. — It  is  employed  to 
decorate  the  facade  of  a  story  of 
small  height,  terminating  the 
upper  part  of  building. 

Attic  Story. — A  term  applied  to 
upn"r  story  of  a  house  wliere  the 
coiling  is  stjuare  witli  the  sides  to 
distinguish  it  from  the  garret. 

Axis.— The  spindle  or  center  of 
any  rotative  motion. 

Bacit.— The  upper  side  of  a  hand 
rail.  (The  under  side  is  termed 
the  /)r«i.st.)  The  term  is  also  ;i  p- 
plied  to  t.l»e  hip  and  conniitin 
I'after,  as  1  lie  back  of  a  hip,  and 
the  Ixwit  of  a  rnfler. 

Bacldiis:  a  lfi|».— 213;  a  practical 
iiK'tliod.  217. 

Baciilns  V^*  a  M'all.— The  term  is 
applii'd  to  bai'kiiig  up  a  wall 
with  brick  or  other  material  when 
the  face  is  veneered  with  more 
expensive  material.  This  should 
be  carefully  done  with  close 
joints,  as  the  mortar  will  shrink, 
and  apt  to  buclcle  the  wall. 


Badi^eon.— A  mixture  of  sawdust 
and  strong  glue  used  to  fill  up  the 
defects  in  woodwork  after  being 
dressed  off.  The  application 
should  be  very  light,  as  it  is 
liable  to  shrink.  A  mixture  of 
freestone  and  plaster  used  by  the 
mason  to  fill  defects  in  dressed 
stonework. 
Balcony.— A  platform  in  front  of  a 
window  or  other  opening,  sup- 
ported on  brackets,  and  made 
safe  by  a  balustrade,  and  shel- 
tered sometimes  by  a  large  pro- 
jecting hood  or  canopy. 
Baluster.— The  vertical  supports 
to  a  hand-rail;  a  small  column 
with  turned  shaft;  standard 
lengths  of,  152;  to  find  the  odd 
lengths  under  the  tangents,  208, 
151,  203:  spacing  around  the  cylin- 
der, 89,  70,  71,  149:  to  find  their 
position  for  boring  on  the  croolv, 
209;  to  find  the  pitch  of  templet 
for  boring,  209;  boring  for  balus- 
ters, best  results,  209. 
Balnstrado.— A  number  of  balus- 
ters pla.'ed  in  a  row  supporting  a 
cap  or  rail.  In  the  colonial  style 
it  has  a  beautiful  elfect  wlien 
used  as  a  cresting  surmounting 
the  cornice  or  a  truncated  roof. 
Banker.— A  bench  on  wliich  the 

stonecutter  worlvs  the  stone. 
Base.  —  The  finish  at  the  floor 
skirting  the  sides  of  a  loom  to 
protect  the  walls.  The  members 
are  for  the  better  class  of  work, 
composed  of  plinth,  mibiMnth, ha.sG 
moulding,  and  shoe  or  quarter 
round,  the  base  being  tongued 
down  into  the  shoe,  and  also  Into 
the  base  moulding. 
Batten.— A  piece  of  wood  from  one 
to  six  inches  wide;  the  horizontal 
pieces  on  a  ledije  or  batten  door,  to 
which  the  boards  are  secured; 
also  used  for  stripping  stone  or 
brick  walls  for  lath  and  plaster. 
Batter.- The  slope  or  inclination 
given  to  a  wall  or  buttress,  as  in 
retaining  walls,  piers  and  abut- 
ments. 
Barge-board.  —  The  board  that 
covets  the  rafters  at  the  gable 
end  of  a  roof,"  in  the  Elizabethan 
style  of  architecture  it  was 
placed  at  the  verge  of  the  raking 
cornice  and  enriched  with  scroll 
work  and  carvings.  It  is  also 
termed  a  vcroc-honrd. 
Bead.— A  moulding  semi-circular 
in  section.  When  the  bead  is 
flush  with  t  hesurf.ace  itis  termed 
a  quirh-bead;  when  raised  it  is 
termed  ticorh-hcad;  when  worked 
from  two  sidf?s  it  is  termed  n  re- 
turned head  or  dovhlc-rpiirlied  head. 
A  seriesof  beads  woi-Ked  {)ar;illel 
to  each  otlier  is  termed  reedinu. 
Beam.— Either  of  timber  or  iron, 
used  to  counteract  a  weight  by 
compression  or  extension.  Wheii 
used  to  resist  the  thrust  of  a 
rafter  it  is  termed  a  tie-hcnm,  the 
strain  being  one  of  tension;  when 
used  as  a  coi?ar  henm.  (see  colltir 
beam),  or  as  a  slrnining  beam,  it  is 
in  a  state  of  compression:  or  if 
used  to  support  the  ends  of  joist. 


Glossary  and  Index. 


m 


Or  as  a  lintel,  the  strain  is  a  trans- 1 
verse  or  cross  strain.  (See  strain.) 
To  find  the  safe  load  for  an  in 
cliniuK  beam,  130;  to  find  the  safe 
load  for  a  horizontal  beam,  225; 
to  find  the  strongest  beam  that 
can  be  cut  from  a  log,  21(i;  the 
best  form  for  rectangular  tim- 
bers, 227. 

Be<l.— The  horizontal  surface  of  a 
brick  or  stone  when  built  in  a 
wall;  when  stone  are  built  in  a 
wall  with  their  laminations  hori- 
zontal they  are  said  to  be  quarry 
headed. 

Bed-SIouldin^.  —  The  moulding 
under  tlie  plancier  of  a  cornice 
carried  around  the  brackets  or 
over  and  in  front  of  the  dentil 
course;  also  in  the  angle  formed 
by  the  shelf  and  frieze  of  a  man- 
tel. 

Belt  Conrse.— The  course  of  stone 
in  a  wall  immediately  above  the 
ground.  It  projects  usually  one 
inch  and  is  also  termed  the 
plinth. 

Bearer.— A  term  piven  to  the  sup- 
port under  a  flight  of  stairs.  Also 
termed  the  carriage  oriouoh  hors€,i. 
(See  Horfting  up.)  To  find  the  di- 
mension of  timber  so  the  soffit  will 
not  deflect  more  than  .03  of  an 
inch  per  foot  of  its  length,  129, 130, 
131 ;  to  calculate  the  load  likely  to 
come  upon  the  bearers,  129;  for 
self-supporting  stairs,  203. 

Belvedere.— A  small  portion  of  a 
building  carried  above  the  roof  to 
view  the  surroundings;  also  term- 
ed a  turret,  lantern  or  cupola. 

Bevel.  —  A  tool  similar  to  a  try 
square,  only  the  blade  is  adjusta- 
ble to  any  angle  with  the  stock. 
Application  to  the  crook  for  the 
twist  of  a  hand  rail,  39,  43,  61,  63; 
crossing  the  tangents  explained, 
67,43,68,  66;  to  prove  the  correct- 
ness of  bevel  and  application,  61, 
170;  for  hip,  valley  and  jack  raf- 
ters, framing,  or  anj'  splayed  work, 
218. 

Beveled.— Two  planers  meeting  at 
any  angle  less  or  greater  than  a 
right  angle.  It  is  termed  splayed 
in  many  cases. 

Btrd's-nioutii.- An  interior  angle 
cut  on  the  end  of  a  timber,  to  flt 
and  rest  on  the  external  angle  of 
another  timber. 

Black  Walnut.— 210;  to  color  the 
sap  part,  210. 

Bioekinss.— Small  pieces  of  wood 
glued  in  the  unexposed  internal 
angles  of  step  and  rise  of  stairs  to 
strengthen  the  joint. 

Block. stone.— Heavy  stones,  as 
they  come  from  the  quarry. 

Bolt.— To  find  the  size  of  bolt  to 
resist  the  strain  likely  to  come 
upon  the  bolt;  divide  the  strain  by 
2,200  and  take  the  square  root  of 
the  product  for  the  diameter  of 
bolt.    (Farey). 

Bond-Course.- In  brick  work  ev- 
ery sixth  course  is  laid  as  a  header 
across  the  wall  to  bind  the  whole. 
In  stone  work,  bond  stones  for 
common  ruble  work  is  usually 
cpecifled,  every  2}^  or  3  feet  super- 


ficial, so  as  to  make  the  whole  ag- 
gregate act  together,  and  be  mu- 
tually dependent  on  each  other. 

Bond-Timber. —Timbers  built  In 
the  walls  to  tie  them  longitudi- 
nal, and  also  to  nail  the  wainscot- 
ing and  other  finish  thereto.  Hoop 
ii*on,  notched  or  serrated  on  the 
edge  and  coated  with  pitch,  and 
built  in  the  wall,  is  preferred,  be- 
ing more  durable  in  case  of  fire. 

Bond->itoiie.«i.— Sometimes  termed 
throiiijli  .^tonex,  are  such  as  extend 
through  the  thickness  of  wall;  in 
good  ruble  work  they  should  be 
built  in  every  S'i  or  3  feet  super- 
ficial of  wall  surface,  and  in  very 
thick  walls  every  course  should  be 
heart  hounde.d. 

Boss.— An  enrichment  at  the  inter- 
section of  groins,  or  cross  vaulted 
ceilings. 

Bossagc.— Stones  that  are  left  pro- 
jecting from  a  wall  to  be  orna- 
mented in  the  future. 

Boudoir.— French,  a  trrm  used 
to  designate  a  room  especially  ap- 

Eropriated  to  the  mistress  of  the 
ouse,  as  her  sitting  room.  (Gwilt). 

Boxing;.- Window  frames  are  such 
when  boxed  out  at  the  sides  to  re- 
ceive sash  weights ;  for  inside 
shutters  in  first-class  houses  the 
jambs  are  boxed,  either  splayed  or 
square  to  the  window  frame,  to  re- 
ceive the  inside  shutters ;  the  shut- 
ters are  then  termed  ho.v  shxittero. 

Brace  or  Strut.  —  An  inclined 
piece  of  timber  forming  a  triangle 
to  give  strength  to  a  building  or 
any  part  of  the  same.  It  is  also 
termed  a  strut.  To  find  the  strain 
from  a  given  load,  229;  from  a 
given  strain  to  find  the  dimension 
of  timber,  229. 

Bracket.— How  to  diminish  the 
size,  27, 105. 

Breadth.— The  greatest  width  of  a 
body  at  right  angles  to  its  length. 

Bressunin»er.  —  The  meaning  is 
restri(^ted  to  a  beam  or  lintel  across 
the  opening  of  a  shop  front,  to 
support  the  superincumbent  load. 

Brick-L.ayers.— Memoranda,  239. 

Brick-Work.  —  'When  brick  are 
laid  in  a  wall  at  right  angles  to  the 
face  of  wall,  it  is  termed  a  header. 
When  laid  parallel  to  the  face  of 
wall  it  is  termed  a  stretcher.  When 
every  alternate  brick  is  laid  as 
stretcher  and  header,  and  to  break 
joints  with  the  next  course  above 
and  also  under,  it  is  termed  Flem- 
Uh  bond. 

Brid{fingr.— Strips  IWXS",  cut  and 
fixed  from  the  lower  edge  of  one 
joist  to  the  upper  edge  of  the  next, 
crossing  each  other,  is  termed  her- 
riny-hone,  tru.'is  or  ci-o.-^s-hridijing. 
The  joist  is  usually  bridged  in  this 
way  every  five  feet  of  their  length ; 
the  strength  gained  by  bi'idging  in 
this  way  is  three  times  over  those 
that  are  not  bridged.  (See  Hat- 
field's Transverse  Stairs). 

Builder. — One  who  contracts  for 
the  erection  and  completion  of  a 
building  in  all  its  parts. 


IV 


Glossary  a.nd  Index. 


Building— An  edifice  constructed 
for  use  or  cou v^enience, as  a  house, 
a  church,  a  shop,  &c. 

Btittr«!<is. — A  pier  or  heavy  pro- 
jection carried  up  to  support  a 
wall;  a  cheif  feature  in  Gotliic 
architecture.  When  carried  from 
one  buttress  to  another  hy  arch- 
ing, as  in  large  niediaaval 
churches,  where  tlie  outer  but- 
tress is  made  to  give  support  to 
the  buttress  of  tlie  clear  story  by 
arching  over  the  roof  of  the  Iri- 
forium  or  gallery,  it  is  termed  a 
flyuKj  huLtreas. 

Beitt-Joiict. — A  joint  at  right  an- 
gles to  the  direction  of  the 
straiglit  part  of  anything,  or  that 
is  normal  to  any  curve  at  its  in- 
tersection with  the  curve;  aterm 
applied  to  tiie  center  joint  of  the 
wreath  rail,  wliich  is  at  right 
angles  to  tlie  tangents  of  two 
wreath  pieces  of  a  hand-rail. 

Cabling-, — A  staff  or  reed  orna- 
ment placed  in  tiie  flutes  at  the 
base  of  a  column,  the  height  of 
same  being  about  one-third  the 
height  of  the  shaft. 

Ciige. — An  outer  work  of  timber 
surrounding  another.  Thus  the 
cage  of  a  stair  is  the  wooden  en- 
closure that  confines  it.  \_NMi- 
olson. 

Camber.— A  slight  arching  given 
to  the  upper  edge  of  joist  about 
'/»"  in  Ifj  feet  of  span. 

Campanile.— In  Italy  a  detached 
tower,  erected  for  the  purpose  of 
containing  bells. 

Canted.— A  position  taken  oblique 
to  the  horizon. 

CaHopy. — See  balcony. 

Casitisig-Strip.— In  frame  build- 
ings the  strip  immediately  above 
the  ba.se-board,  and  on  which  the 
weather  boarding  and  corner 
strips  rest;  it  is  canted  so  as  to 
carry  the  water  from  the  build- 
ing. It  is  also  termed  a  water 
taJM. 

Cantilever.— The  joist  that  are 
made  to  extend  out  fi'oni  a  build- 
ing to  support  a  balcony  or  coi-- 
nice;  sometimes  termed  foofrowts. 

Capital  .—The  crowning  division 
of  a  column.  In  classic  archi- 
tecture the  different  orders  have 
their  respective  capitals;  but  in 
the  Egyptian,  Indian,  Byzantine 
and  Gotliic  architectures  there  is 
an  endless  variety. 

Carpenters.- -Memoranda,  244. 

Carpentry  and  Joinery.— 212- 
223;  descriptive,  212;  mechanical, 
224. 

Carpet-Strip.— Tlie  strip  under  a 
door  wlien  closed,  allowing  tlie 
door  to  clear  the  carpet  when 
open;  also  ter^iied  threslwld,  or 
Kadille  .strips. 

C«sen»ent.— A  glazed  sash,  made 
to  open  and  shut  on  hinges. 

Carving:.- When  carving  stands 
out  from  its  ground  it  is  termed 
in  alto  relievo;  when  projecting 
one-half  it  is  termed  in  mezzo  re- 
lievo ;  and  when  slightly  raised  it 
Is  termed  basso  relievo,  which  is 


the  opnosito  when  carved  in  in- 
ttiglif),  or  sunk. 

Carcase.— A  building  roofed  in; 
ready  for  the  joiner,  plasterer 
and  other  artizans  to  ornament 
and  complete  the  work. 

Caul.— A  devise  used  hot  in  ve- 
neering to  press  the  veneer  close 
to  the  form,  and  at  the  same  time 
keep  the  glue  moist  in  circular 
work.  The  caul  is  made  to  the 
curvature.  At  other  times  bags 
of  sawdust  are  used,  being  ea.sily 
adjusted  by  clamping  to  the  re- 
quired curve. 

Cavetto.  —  A  hollow  moulding 
whose  profile  is  a  quadrant  of  a 
circle  and  iatei-ined  a  cove  mould- 
ing. It  is  the  scape  from  the  shaft 
at  the  base,  and  al.so  from  the 
shaft  to  the  capital  of  a  column. 
It  is  also  termed  the  apojjoge. 
IWeal^.l 

Centering:. — Temporary  supports 
over  which  arches  and  vaults  are 
constructed;  they  are  chiefly 
built  of  wood. 

Cliancel- Kail. —The  rail  and  bal- 
usters around  the  chancel  or 
altar  in  churches,  and  the  bar  in 
the  courts  of  justice. 

Chamfer.  —  An  arris  reduced 
equally  on  both  sides  forming 
two  obtuse  angles.  If  the  cham- 
fer is  stopped  short  at  the  end,  it 
is  then  tei'med  a  stop  chnmfer. 

Chimney.— An  appendage  to  the 
house  in  which  the  fire  place  is 
located  and  serves  to  convey 
away  the  smoke  and  ventilate 
the  rooms. 

Chord.— 24. 

Cheveron.— A  moulding  having  a 
zig-zag  orsorrated  edge;  peculiar 
to  the  Norman  style;  it  is  also 
termed  a  zig-zag  and  dancette 
moulding. 

Circular  Winding:  Stair-Case— 
A  stair-case  that  is  circular  on 
plan  liaving  all  the  steps  wind- 
ing. If  the  steps  are  supported 
by  a  wall  at  one  end  and  open  at 
the  other,  it  is  termed  a  (ieomel- 
rical  stair-case.  198. 

Circle.— To  find  the  area,  2-3,  24; 
circumference,  23. 

Cincture.  —  A  fillet  or  narrow 
band  connecting  one  moulding 
with  another,  as  the  caretto  at  the 
top  of  a  column  is  connected  with 
the  astragal,  or  at  the  base  with 
the  torus 

Clamp.— A  narrow  piece  of  wood 
joined  to  the  end  of  a  wide  piece 
to  prevent  its  warping;  a  device 
with  screws  used  when  gluing 
two  pieces,  to  force  out  the  sur- 
plus glue  from  the  joint. 

Cleat. — A  narrow  strip  of  wood 
nailed  on  in  joinery;  as  apiece 
of  wood  nailed  on  a  door,  a  shut- 
ter, &c     \_Wehster. 

Close-Outer-String.  — Is  meant 
that  the  steps  and  risers  are 
housed  into  the  outer  string, 
same  as  the  wall  string.'  When 
such  is  the  case  the  face  of  outer 
string  is  either  paneled  or  other- 
wise ornamented  with  string 
mouldings,  instead  of   brackets 


Gt.ossary  and  Index. 


and  return  nosings,  as  in  open 
strings.  210,  211. 

Closer. — A  brick  eitlier  less  tlian 
a  iialf  or  a  whole  brick,  used  to 
close  up  a  course  of  brick  worlt ; 
when  less  than  a  whole  brick  and 
greater  than  a  half  brick,  it  is 
called  a  kiiio  closer;  when  less 
than  a  half  brick,  it  is  tei-nied  a 
queen  doner. 

Cockle-Stairs.— A  term  used  to 
denote  a  winding  or  spiral  stairs. 
iChamhers). 

Coffer.— A  deep  sunk  panel  in  a 
ceiling,  dome  or  vault.  It  i8  also 
termed  Cai.smn. 

Collar.  Beam.  —  A  beam  used 
above  the  lower  end  of  rafters  to 
cut  off  the  angle  of  rafters  at  the 
ridge,  and  also  to  stiffen  the  roof. 
If  there  be  a  tie-bearer,  then  the 
collar-bearer  is  in  a  state  of  com- 
pression ;  i  f  no  tie-bearer,  then  the 
strain  is  one  of  tension. 

Column.— A  long  round  body  of 
wood,  stone  or  iron;  the  part  on 
which  it  rests  is  termed  the  /;a.st'. 
The  heart  is  termed  the  capital,  and 
the  intermediate  part  is  termed 
the  tfhaft.  The  capital  is  sur- 
mounted by  the  ohacris  immedi- 
ately on  which  the  arc/iitrare  rests. 
There  are  five  orders  of  column 
the  Tuscan,  Doric,  Ionic.  Corin- 
thian and  the  Composite.  The 
column  was  a  chief  decorative  fea- 
ture in  the  porticoes  of  the  an- 
cient Greeks  and  Romans.  They 
are  termed  engaycd  or  attached  c^>l- 
umns  when  projecting  three-quar- 
ters or  less  from  a  wall,  and  (»i,sm- 
lated  columns  when  they  stand 
clear  of  the  walls. 

<'oinmon  Hafter,— The  rafter  to 
which  the  sheathing  is  nailed;  it 
is  supported  by  the  purlin,  which 
in  turn  are  supported  by  the  prin- 
cipal rafters,  in  a  trussed  roof. 

Common  Rafter.— 315. 

Concentric. —  Circles,  24,  and  el- 
lipses, 33. 

Concrete.— Proportions  of  cement 
and  stone,  238. 

Concave.— 34.  and  Convex,  24. 

Cone.— Eule  to  find  the  area,  29. 

Conic  Sections.— 29,  30. 

Conge.- A  co^e.  same  as  the  apo- 
poge  and  the  Cavetto. 

Console.— An  ornamental  bracket 
placed  on  the  pilaster  of  a  frontis- 
piece to  support  the  cornice;  also 
to  ornament  the  keystone  of  an 
arch;  termed,  also,  Ancone  and 
Trvsses. 

Conservatory.— A  building  for 
the  propagation  and  preserva- 
tion of  rare  plants  and  flowers. 
A  superior  greenhouse,  it  should 
be  in  a  very  dry  situation,  and 
the  walls  should  be  at  least  three 
bricks  thick.    [Stuart. 

Coping^. — A  course  of  stone  or 
wood  on  top  of  a  wall  for  a  pro- 
tection. When  the  coping  is  one 
thickness  it  is  termed  par-allel 
coping;  when  thicker  in  the  mid- 
dle and  the  top  slanting  two  ways 
it  is  termed  saddle-baeh  coping; 
when  thinner  on  one  edge  than 


the  other,  it  is   termed  feather- 
edge  coping. 

Corbel.— A  term  denoting  a  pro- 
jecting stone  or  piere  of  timber 
which  supports  a  weight  or  strain. 
A  row  of  corbels  connected  with 
small  arches  or  otherwise  is 
termed  a  corbel  table. 

Cornice. — The  upper  division  of 
the  entablature  directly  over  the 
frieze;  when  the  frieze  is  omitted 
the  cornice  is  termed  an  archi- 
trave cornice. 

Corona.— The  outer  fascia  of  a 
cornice  to  which  the  crown 
moulding  is  nailed;  the  corona  is 
allowed  to  drop  below  the  plan- 
cier,  and  thus  form  a  drip. 

Corridor.— A  passage  or  gallery, 
from  which  an  entrance  may  be 
had  to  various  apartments;  some- 
times running  around  a  quad- 
rangle. 

Coved-Ceiling.— The  walls  of  an 
apartment  made  to  join  the  cell- 
ing with  a  curve  instead  of  a 
right  angle. 

Crockets,— Ornaments  of  foliage, 
or  animals  used  to  decorate  the 
angles  of  spires,  pinnacles  or  ga- 
bles. 

Crown  nionldingr>  — The  upper 
moulding  of  a  cornice,  the  cyma 
recta  being  mostly  used  for  that 
purpose,  as  it  forms  a  good  water 
drip. 

Crossetts.- The  projection  or  ears 
on  arch  stones  to  allow  one  arch 
stone  to  bang  on  the  adjacent 
stone;  the  breaks  in  architraves 
around  openingr,  as  doors,  win- 
dows, &c. 

Curtail-Step.— The  first  step  in  a 
stairway  when  the  end  is  finished, 
in  the  form  of  a  scroll;  also  termed 
the  scroll  step;  how  to  draw,  33; 
manner  of  constructing.  35. 

Cupper  Gauge.— Construction  of, 
99. 

Cupola.  —  A  dome  or  spherical 
vault  crowning  an  edifice. 

Cutting  Plane.— A  plane  cutting 
a  solid  into  two  parts  in  any  direc 
tlon.  In  hand  railing,  the  plane 
on  which  is  developed  the  face- 
mould  for  the  wreath-piece,  38.  43, 
48,  51,  54,  47. 

C.vlindcr,— In  geometry,  a  solid 
flsfure  whose  base  is  a  circle  and 
whose  curved  superflces  is  every- 
where at  an  equal  distance  from 
the  axis  or  line  supposed  to  pass 
through  the  middle.  The  term 
throughout  this  book  is  applied  to 
the  wreath  or  circular  part  of  the 
outer  string.  To  find  the  location 
of  rises  in  a  jjlatform  cylinder,  so 
the  wreath-piece  will  raise  the 
proper  height  without  springing 
the  plank,  144;  to  determine  the 
position  of  risers  in  a  platform 
cylinder,  so  the  inclination  of  rail 
will  have  the  common  pitch  on  the 
center  lino  of  rail,  70;  to  establish 
the  position  of  rise  in  a  quarter 
cylinder,  so  the  wreath-piece  will 
raise  the  proper  heighten  the  level 
and  not  spring  the  plank.  144;  to 
locate  the  position  of  rise  In  a 
quarter  cylinder,  so  the  wreath- 


v> 


Glossary  and  Ixdex. 


piece  may  be  constmeted  in  one 
piece  when  there  are  llyers  above 
au"l  below  the  cylinder.  71,  T;J;  to 
flud  the  position  of  risers  in  a 
quarter  cylinder  having  flyers 
iihove  and  below,  so  that  two 
wreath-pieces  may  form  the  twist, 
and  that  they  m;iy  be  constructed 
from  the  least  thickness  of  plank, 
73;  to  find  the  position  of  risers  in 
cylinders,  so  the  wreath  part  of 
outer  siring  may  have  the  same 
inclination  as  the  straight  part,  70. 
09,  100;  to  determine  the  location 
of  risers  in  a  cylinder  at  turnout, 
84,  119,  123. 120;  number  of  staves 
in  a  platform  cylinder,  149;  ve- 
neering a  cylinder  over  a  drum, 
I'A,  155;  thickness  of  vencrr,  rule 
for,  125;  dadoing  and  bending  over 
a  drum,  127;  distance  apart  to 
make  the  grooves.  127;  glueing  up 
staves,  102,  10:3;  that  is,  veneered, 
127;  how  to  place  the  risers  in  a 
semi-circular  cylinder  starting  and 
landing,  so  that  one  set  of  face- 
moulds  will  answer  for  both 
wreaths,  73.  75;  how  to  place  the 
risers  when  less  or  more  than  a 
quarter  circle,  80;  bow  to  place 
the  risers  in  platform  cylinders. 
69;  how  to  place  the  risers  in  a 

f)latform  cylinder  on  the  center 
ineof  rail.  70;  joints  of  cylinder. 
121;  to  find  the  length  of  staves, 
122,  123, 124, 165. 

Cyina-reeta.— An  Ogee  moulding 
with  the  concave  portion  above. 
When  the  convex  part  is  above,  it 
is  termed  a  cyma-reversa  moulding 
or  talon. 

DimIo.— The  middle  division  of  the 
pedestal  of  a  column,  termed  tlie 
die.  The  term  is  also  applied  to 
the  wainscoting  around  a  room, 
vestibule  or  hall.  (See  pedestal.) 
A  plane  also  termed  cuttinfj- 
thrush ;  used  to  cut  grooves  in  a 
board  across  the  grain,  termed 
dadoint)  or  (jaininu-  150. 

Damp-Course.— A  course  of  slate 
or  asphalt  laid  iu  cement  on  out- 
side walls  about  18"  above  the 
earth  surface  to  prevent  the 
dampness  rising  in  tlie  wall. 

Dead  Sliore,— An  upright  piece 
of  timber  built  in  a  wall  to  sup- 
Dort  a  superincumbent  weight 
until  the  brick  which  is  to  carry 
the  load  has  set  or  become  hard. 

Dentils.— Small  cubes  resembling 
teeth  arranged  in  a  course  to  or- 
nament a  cornice  or  plain  sur- 
face. Their  width  is  one-half  the 
length,  and  the  space  between 
eacli  dentil  is  one-half  their 
width,  and  the  pro.ioction  is  equal 
to  their  face  width. 

Details.  —  Drawings  made  to  a 
large  scale  or  full  size,  furnished 
by  the  architect  to  tlie  builder, 
and  termed  workinu  drawimj^. 

Diag'Oiial. — 32. 

Diameter. — 24. 

Dimension.- The  length,  breadth 
or  thickness  of  a  body. 

Directing  Ordinate.  —  A  line 
th.at  governs  the  direction  of  an 
ordinate.  43,  44. 


Discliargring  Arch.  —  An  arch 
built  in  a  wall  over  a  lintel,  or 
above  another  arch  to  discharge 
the  weight  to  the  piers.  Also 
termed  a  relieving  arch. 

Dog-lLeifg-ed  Ntairs.  —  Such  as 
are  solid  between  the  upper 
flights;  or  those  which  have  no 
well  hole;  the  center  of  rail  and 
balusters  of  the  dilferent  flights 
being  in  one  plane. — [Nichohion. 
86-93. 

Dome. — A  circular,  elliptical  or 
polygonal  covering  of  a  part  or 
whole  of  a  building.  The  dome 
of  the  Pantheon  at  Kome  is 
spherical  in  form,  and  1423^  feet 
in  diameter. 

Door.— The  entrance  into  a  house 
or  an  apartment. 

Door-Frame — The  wooden  jambs 
and  head  enclosing  a  door;  also 
including  the  sill  if  made  of  wood. 

Dormer  — A  window  in  the  roof 
of  a  house  having  the  frame  in  a 
vertical  position.  When  the  win- 
dow lies  in  the  plane  of  the  roof 
it  is  termed  a  skylight. 

Dormitory. —  A  large  sleeping 
apartment  containing  many 
beds. 

Dove-Tail.- A  tenon  in  the  .shape 
of  a  dove's  tail  which  is  made  to 
flt  into  a  mortise  shaped  like  a 
trapezoid,  forming  a  joint  mucli 
used  by  cabinetmakers  in  mak- 
ing drawers,  boxes,  &c.  104,  105; 
pattern,  98. 

Dowel.— A  pin  used  in  a  joint  fo 
give  strength  and  prevent  the 
joint  from  shifting,  termed ttowe!- 
iny  the  joint.  98. 

Dragon  Bean»— A  sliort  beam 
forming  a  seat  for  the  foot  of  a 
hip  rafter,  and  is  held  in  ijlacc 
by  the  mujU  tie. 

Draught- Board. — And  draught- 
ing instruments,  3. 

Drawing-Knife.— 37. 

DrawiiiifS. — In  carpentry  the  de- 
scription of  a  building  made  on 
paper  to  a  scale,  describing  the 
dilferent  parts  thereof,  both  in- 
terior and  exterior,  by  plans,  ele- 
vations, cross-sections  and  details. 
They  are  considered  the  prop- 
erty of  the  architect  when  the 
building  is  completed. 

DrawJnar-Roona. — The  room  to 
which  the  company  retire  after  a 
meal. 

Draw-Bore  and  Pin.— In  fram- 
ing, the  hole  through  the  tenon 
is  bored  closer  to  the  shoulder  by 
Vi"  than  the  hole  in  the  header  is 
from  the  cheek;  this  allows  the 
oak  pin  to  draw  the  shoulders  up 
close.  When  the  tenon  extends 
through  and  the  pin  driven  on 
the  outside  of  trimmer  it  is  term- 
ed througlihore  and  pin. 

Dressinp-s- In  abrick  front, stone 
is  often  used  for  lintels,  sills, 
arches,  quoins,  cornices,  termi- 
nals, string  courses  and  otlier 
facings,  which  is  termed  stone 
dre-tsings.  The  front  may  be  of 
stone  and  brick  or  terracotta  used 
for  dressings;  if  wood  be  used  it 
would  be  termed  wooden  dressings. 


Glossary  and  Index. 


Dwarf  Walls.— Low  walls  of  less 
height  than  the  story  of  a  build- 
ing; sometimes  the  joist  of  a 
ground  floor  rest  upon  dwarf 
walls;  and  the  enclosures  of 
courts  arc  frequently  formed  by 
them,  with  a  railing  of  iron  on 
their  top. — [NichnUon. 

Die  or  Dye.— The  plain  shaft  of  a 
pedestal. 

Eav«.— The  lower  edge  of  a  roof 
which  overhangs  the  wall  to 
carry  the  drip  beyond  its  outer 
surface.  The  eave  course  in 
shingling  should  be  in  three 
thicknesses  tapered. 

EaHiiiff.— To  draw.  161,  163,  1G.5; 
pattern  to  make  for  cutting 
straight  rail,  111,  138;  starting 
from  a  newel,  114. 

Cchiiius.— An  ovolo,  a  member  in 
the  capital  of  a  column  under  tlie 
abacus,  which  is  carved  into  the 
egij-and-ilart  niouldiny ;  also  term- 
ed einj-iutd-tonijue  or  egg-andan- 
chor  moulding. 

£lli|>sis.— To  draw  with  a  tram- 
mel, 31;  with  a  string,  3:2;  straight 
edge,  31;  described  on  the  cutting 
plane,  31:  rule  to  lind  the  area, 
31;  and  also  the  circumference,  31. 

£ilipiic.  —  Winding  stairs  and 
manner  of  constructing  the  same, 
203,  201. 

Embattled  Biiildin;;.  —  Resem- 
bling a  castle  having  merlons  and 
emhni^urets  on  the  top  of  walls, 
forming  a  parapet  above  tiie  roof, 
as  in  castelated  architecture  in 
mediajval  times. 

Einbo^sted  Work.  —  In  Gothic 
architecture  a  kind  of  sculptured 
work;  the  figure  is  raised  and 
chiseled  into  foliage  heads  and 
animals,  serving  as  a  .sfop  at  the 
intersection  of  ribs  in  groined 
ceilings,  and  also  weather  mould- 
ings around  doors  and  windows. 
Any  raised  figure  relieving  a 
plain  surface  may  be  termed  em- 
bossed work. 

Knibrasure.  —  Also  termed  Crc- 
ncUrs;  ilie  spare  between  the  mer- 
lons, for  the  battery  iu  ancient 
miliiiiry  architecture. 

Eende4-a;;4>n.  —  A     polygon     of 

eleven  sifh's. 
Eiilablat lire.— The  whole  of  the 
parts  of  an  order,  above  the  aba- 
cus;   in  the   Greek,    Roman    and 
Italian  architecture  it  is  divided 
into  three  divisions,  the  architrave, 
frieze  and  cornice. 
Entasis.-  la  the  Greek  classic  or- 
ders, a  slight  swell  in  the  shaft  of 
a  coluniu  or  baluster 
Kqiiilalerjil.— triangle.  23. 
Es«'a|>e.-  The  cove  at  the  bottom 
and  top  of  the  shaft  of  a  column, 
where  the  shaft  e.'^cajics  from  the 
l:>asc,  and    also   the   capital;  also 
termed  the  apoplnjuc. 
Kx.lornal  AMjflp,"— 22 
Excavalorx.— Memoranda,  236. 
Eye.— Eye  of  a  scroll  is  the  circle 
from  which  the  spiral  line  com- 
mences; the  center  of  a  volute, 
35,  36 
Facade.  —  The    main   front  of  a 
building. 


Face-Moald.— The  profile  of  a  cyl- 
indric  section  as  it  is  developed  on 
the  cutting  plane;  the  pattern 
is  used  to  line  off  the  crook  for 
the  wreath-piece  of  a  hand-rail: 
to  draw  for  a  turnout  slightly 
inclining  at  the  newel,  152,  153; 
for  a  turnout  level  at  the  newel, 
109, 110;  for  level  to  a  rake,  73,  77, 
135;  for  rake  to  a  level,  73,  80,  133; 
for  platform  twist,  111;  without 
springing  the  plank,  114;  when 
the  risers  are  misplaced,  110,  113; 
when  the  pitch  off  the  platform 
is  different  to  the  pitch  to  the 
platform,  to  draw  one  mould  to 
answer  for  both  wreath-pieces, 
116;  for  a  quarter  turn  starting 
and  landing,  110,  111;  for  over 
winders  in  a  cylinder  greater  than 
a  quarter  circle,  starting  from  a 
newel,  180,  181;  to  connect  the 
straight  rail  at)ove  and  below  the 
quarter  pace,  80,  82;  for  winders 
in  a  senu-circle  having'  two 
wrealh-pieces,  107,  168,  18:3,  184; 
for  winders  in  a  semi-circle  hav- 
ing three  wreath- pieces,  193;  for 
winders  in  a  quarter  circle  to 
connect  the  straight  rail  above 
and  below  the  quarter  circle  and 
work    the   ramp    in  the    wreath 

Eiece,  138;  for  a  quarter  circle 
aving  windei's  starting  from  a 
newel,  185;  to  draw  over  winders 
to  contain  the  easing  connecting 
the  straight  rail  at  the  upper  or 
lower  end,  187,  138;  for  a  circular 
well  hole  on  plan,  198:  elliptical, 
203,  209,  64,  69;  wreath-piece  with 
a  full  easing  for  a  quarter  circle 
on  plan,  130, -37;  for  a  wreath-piece 
with  an  intermediate  easing  for 
a  quarter  circle  on  plan,  41;  for 
a  wreath-piece  with  no  easing 
over  a  quarter  circle  on  plan,  46: 
for  a  wreath-piece  with  a  full 
easing  over  a  less  than  a  quarter 
circle  on  plan,  49;  for  a  wreath- 
piece  with  an  intermediate  eas 
ing  over  a  less  than  a  quarter 
circle  on  plan,  53;  for  a  wreath- 
piece  with  no  easing  over  a  less 
than  a  quarter  circle  on  plan,  56; 
for  a  wreath-piece  with  an  inter- 
mediate casing  over  a  greater 
than  a  quarter  circle  on  plan,  62; 
for  a  wreath-piece  with  an  inter- 
mediate easing  over  an  elliptic 
curve  on  plan,  (55:  for  easing  pat- 
terns andwreath-piece  for  a  wall 
rail  on  the  wide  end  of  winders 
in  box  stairs,  95;  for  6"  to  20"  plat- 
form cylinders,  1.34,  135;  for  a 
wreath  over  winders  in  a  cylin- 
der struck  from  different  radii, 
196;  to  draw  so  that  one  set  of 
moulds  and  bevels  will  answer 
for  a  wreath  starting,  and  also 
landing,  the  plan  being  a  semi- 
circle, 75;  to  draw  so  that  one  set 
of  moulds  and  bevels  will  answer 
for  a  wreath-piece  starting  or 
landing  over  a  plan  le.s.s  or 
greater  than  a  quarter  circle,  76, 
80;  to  draw  for  the  wreath  part  of 
a  plaster  moulding  underneath 
the  wreathed  part  of  outer  string. 
1.57;  application  to  the  plank,  for 
sawing   out  the   crooks,   51,   57: 


VIU 


Glossary  and  Index. 


sliding  the  face-mould  on  the 
crook  39, 44, 48, 51,55, 58,112, 113  long- 
est tangent  to  be  taken  first  when 
drawing  the  face-mould,  50;  cor- 
rect points  on  radial  lines  for  the 
trace  of  mould,  50;  over  winders 
in  a  semi-circle  starting  from  tlie 
level,  170;  over  winders  in  a 
semi-circle  landing  on  the  level, 
172;  instructions  in  locating  the 
Inclining  tangents  in  elevation 
over  winders  for  the  falling  line 
of  rail,  189;  points  on  the  joints 
not  the  correct  points  througli 
which  the  curve  will  pass,  54,  56; 
the  block  pattern  does  not  give 
the  correct  contour  of  the 
squared  section  of  wreatli-piece 
when  the  .joint  is  made  from  an 
inclining  tangent  in  the  curved 
part  of  wreath-piece,  40,  49;  when 
drawing  the  face-mould  by  this 
method  take  the  longest  tangent 
first,  50. 

Factor  for  Safety.— 225. 

FalliusT  lilne.— An  imaginary  line 
passing  through  the  center  of  a 
wreathed  hand-rail,  as  may  be  con- 
ceived in  the  center  of  a  round 
rail;  in  the  tangent  system  of 
hand  railing  the  falling  line  an- 
swers to  the  center  elliptic  curve 
on  a  face-mould,  and  may  be  so 
termed  the  falling  line  of  the 
wreath  rail,  IT3. 

Fnllin;;  Mould— A  parallel  mould 
made  equal  to  the  depth  of  rail, 
and  from  pasteboard  or  other  flex- 
ible material,  used  to  trace  the 
twist  lines  of  a  wreath-piece  by 
bending  the  same  around  the  vei'- 
tical  sides  of  a  cjiiudric  section  af- 
ter being  worked  off  to  the  pitch 
bevel,  then  tracing  the  upper  and 
lower  sides  of  rail;  the  old  masters 
used  two,  one  lor  the  inside  and 
the  other  for  the  outside,  41. 

FaHCia.— The  level  casing  of  the 
joist  around  the  well  hole  of  a 
staircase  is  termed  the  kvcJ  fascia. 
In  a  cornice  the  baud  under  the 
planceer  is  termed  the  hack  fascia 
and  the  band  under  the  crown 
moulding  which  drops  down  below 
the  planceer  is  termed  the  front 
faticia.  In  the  classic  orders,  the 
back  fascia  is  termed  the  frieze; 
and  the  front  fascia  is  termed  the 
corona. 

Festoon.— Dr.ipery,  garlands  knot- 
ted at  intervals,  much  used  in  the 
classic  style  of  architecture  in  dec- 
orating the  frieze  of  the  Ionic  and 
Corinthian  orders.  The  garlands 
are  heaviest  at  the  centre  and  ta- 
per towards  the  points  of  8usi)en- 
sion. 

Fillet.  —  A  narrow  flat  band;  it 
marks  the  division  of  the  flutes  in 
the  Ionic  and  Corinthian  columns, 
but  is  missing iu  the  Doric  colunui, 
where  the  flutes  sire  allowed  to  in- 
tersect, forming  one  arris  instead 
of  two,  as  iu  the  former. 

Flnlal.  —  The  bunch  of  foliage 
which  terminates  pinnacles,  cuno- 
pies,  pediments,  &c.,  in  Gothic 
architecture.— L/'fir/fcr. 

FInisli.— A  term  in  joinery  for  the 
iutcrior  finishing  of  a  house  such 


as  doors,  architra%^es,  mouldings, 
base,  &c. 

FIre-Place.— The  place  in  a  room 
for  the  Are.  The  stone  under  the 
Are  is  termed  the  hearthstone.  The 
peri)endicular  sides  are  termed 
the  jambs.  The  grate  contains  the 
Are,  and  the  ornamental  iron  work 
arou  nd  the  fire  place  is  termed  the 
aratc-front. 

Fish-PIato.— A  piece  of  wood  or 
iron  bolted  on  to  the  sides  of  a 
scarfed  tie-beam  to  prevent  the 
joint  from  pulling  apart. 

Flanjfe.— A  projectinir  rib  or  rim 
for  strength,  as  a  guide,  or  for  at- 
tachment to  another  object.— 
Kniiiiit's  American  Mechanical  Dic- 
tionary. 

Flasliing'.- In  a  roof,  pieces  of  tin 
or  lead,  shingled  or  slated  in  and 
turned  up  along  the  walls  and 
chimneys  to  prevent  the  rain  and 
snow  from  beating  in.  In  good 
work  cap  ffashina  is  built  in  tlie 
walls  and  turned  down  over  the 
flashings,  89- 

Flexible.  —  That  which  has  the 
property  of  bending;  contrary  to 
stiftnoss  and  brashness. 

Flig^ht  of  Stairs. —  A  series  of 
steps  from  one  landing  to  another. 
A  one-story  staircase  may  be  com- 
posed of  one,  two  or  more  flights, 
and  arc  designated  as  the  lower, 
upper,  or  middle  flight  (as  the  case 
maybe)  of  the  staircase.  If  the 
flight  runs  from  story  to  story  it  is 
termed  one  fliylit  of  stairs.  If  there 
is  one  half  pace,  it  is  termed  two 
fligJils  of  stairs.  If  the  staircase  is 
divided  into  two  quarter  paces,  it 
is  termed  a  staircase  of  three 
Uiuhts. 

Floors.— Load  likely  to  come  upon, 
139. 

FSii«ili  .foints.— In  masonry,  when 
the  stones  chip  off  at  their  hori- 
zontal joints,  because  the  stones 
are  allowed  to  pinch  at  their  outer 
edge,  being  dished  out  in  their 
beds.  In  joinery,  two  surfaces  are 
said  to  l)e  flush  when  both  form  a 
junction  even  and  parallel,  having 
the  same  plane  as  the  frame  work 
of  a  door  when  ready  for  the  pain- 
ter. 

Fl  H  tcs  —Vertical  coves  on  the  shaft 
of  columns.  The  Doric  column 
has  twenty  flutes  arouud  the  shaft ; 
the  Ionic,  Corinthian  and  Com- 
posite have  twenty-lour;  the  Tus- 
can has  none. 

Flycr«.— The  straight  steps  iu  a 
stair-case  are  termed  Jlyers,  in  con- 
tradistinction to  winders. 

Focus.— 31. 

Fol4liiii;-noor.  —  The  term  do- 
notes  such  doors  that  are  hung  in 
pairs  and  fold  at  the  center  from 
opposite  jambs;  the  rebate  on  one 
side  is  made  to  fold  on  the  other, 
and  a  Itead  worked  on  the  arris  to 
hide  the  joint;  inside  and  outside 
shutters  fold  on  each  other  in  the 
same  manner.  There  may  fje  two, 
three  or  more  do<jrs  folding  from 
the  one  jamb.  Two  wedges  tliat 
cntfr  an  orifice  from  oi)posite 
sides  are  termed  foldinu  vjcdyca. 


GLOSSAr.Y   AND   IXDEX. 


iX 


Folinjjo.— An  ornamental  distribu- 
tion of  leaves  on  various  parts  of 
a  building,  as  on  panels,  rosettes, 
bosses,  corbels,  capitals,  &c. 

Foliate*!.— Gotbic  eusped  tracery 
formed  of  tre-foils,  quarter-foils 
and  cinque  lolls. 

Footiiigrs.— The  first  stones  in  the 
foundation  of  a  wall.  They  are 
large,  heavy  and  project  six  inches 
or  more  beyond  the  next  course 
above  to  distribute  the  load  over 
a  greater  surface  of  ground,  and 
thus  give  greater  security  to  the 
superstructure.  There  may  be 
two  or  more  offsets  to  the  foot- 
ings, according  to  the  weight  of 
the  superstructure  and  the  com- 
pressibilitj-  of  the  soil;  provided 
for  in  the  New  York  and  Chicago 
building  laws.  237. 

Fox-Tail  «leil^e.  —  In  fox -tail 
wedging  the  mortise  is  increased 
at  the  bottom  in  the  direction  of 
the  grain;  then  the  tenon  is 
checked  and  a  glued  wedge  in- 
serted and  allowed  to  project; 
then  afterwards  driven  home. 
This  method  of  joining  is  used  by 
the  chair  makers,  and  is  suitable 
in  spindle  work. 

Fouiidntioii.— The  ground  as  pre- 
pared, either  mother  earth,  piling, 
concrete,  timbering,  planking,  or 
by  any  other  meaBS  on  which  to 
lay  the  foundation  stones. 

Frumer.— In  carpentry,  one  that  is 
expert  in  the  construction  of 
frame  buildings  and  heavy  tim- 
bered structures,  such  as  trussed 
roof.s,  wooden  bridges,  factories, 
rolling  mills,  &c.,  is  known  as  a 
yiiod  framer. 

Freestone.— Any  stone  that  works 
freely. 

Frieze.— A  broad  surface  under  a 
projecting  cap  or  cornice.  In  the 
classic  orders,  the  middle  division 
of  the  entablature  usually  orna- 
mented with  sculpture.  The  wide 
space  under  the  shelf  of  a  mantle 
between  the  fire  front  and  the 
shelf  on  which  the  bed  moulding 
rests.  The  upper  panel  in  a  six 
panel  door  is  termed  a //icze  panel, 
and  the  rail  under  is  termed  the 
frieze  rail. 

Fnrnltnre — In  architecture,  the 
visible  brass  or  other  metallic  fur- 
nishmentof  hardware  for  a  house, 
as  locks,  bolts,  binges,  knobs, 
latches.  &c. 

Fiirring-oul.— Trimming  out  the 
joist  around  hearths  to  tlie  proper 
length  for  the  hearth-stones,  or 
for  the  lathers  where  the  joist  or 
scantling  have  not  been  properly 
spaced,  or  in  corners,  for  solid  nail- 
ing, or  where  in.side  shutters  are 
to  shut  into  a  box,  the  walls  have 
to  he  furred  out ;  also  stone  walls, 
to  avoid  dampness,  are  furred  out 
for  the  lath  and  plaster. 

Gable.— The  triangular  space  at 
the  end  of  a  house  from  the  level 
of  the  eaves  to  the  ridge.  It  is 
termed  a  pediment  when  it  does 
not  rise  the  height  of  the  main 
roof.  When  the  triangular  space 
is  cut  off  by  the  continuation  of 


the  corona  of  the  level  cornice,  the 
triangular  panel  Is  termed  the 
tympanium. 

GHblet.— A  small  gable  used  in 
skew  blocks,  crow-stepped  gables, 
intakes,  on  buttresses,  pinnacles, 
&c.,  for  ornament. 

Gain  — In  joinery,  housing,  the  ex- 
cavation made  in  a  door  or  window 
head  to  admit  the  stiles  their  full 
thicku(.'ss,  and  also  wedge  room 
for  keying  up;  termed  also  dado- 
intj. 

Gag'ned  Arcb.— When  the  stones 
or  bricks  of  an  arch  radiate  to  a 
common  center  it  is  termed  a 
gatjued  arch;  and  the  bricks  are 
termed  gaijued  hrichs,  being  cut 
and  rubbed  until  a  perfect  joint 
and  taper  is  attained. 

Gallery.— The  projecting  stories 
around  the  walls  of  a  theater  are 
termed  galleries.  A  room  for  the 
purpose  of  exhibiting  pictures  is 
termed  a  picture  gallery;  also 
churches  to  increase  the  seating 
capacity  project  plattVjrms  from 
walls  on  three  sides  termed  gal- 
leries That  part  in  which  the  sing- 
ers perform  is  termed  the  siiigers' 
gallery. 

Garret.— The  room  under  the  roof 
of  a  house,  being  lathed  and  plas- 
tered to  the  cellar  beams,  rafters 
and  ashlerings. 

Gas-Fitter.— (See  plumber.) 

Geometrieal  S<tHir-€ase.  —  A 
stair-case  having  one  end  of  the 
steps  supporced  by  the  wall  only 
at  one  eud,  the  other  end  being 
free  between  the  stories,  with  the 
rail  continuous.  If  the  steps  are 
winding  it  is  termed  a  geometrical 
windiugstairx. 

Geometry.— The  science  of  exten- 
sion, quantity  or  maguitude,  22. 

Gin. — A  portable  hoisting  machine, 
having  three  legs,  one  being  move- 
able,used  for  lifting  heavy  weights 
from  wells,  or  building  low  walls. 

Girder. — A  main  beam  to  span 
openings  and  transmit  heavy  loads 
from  support  to  support.  When 
the  loads  are  very  heavy  they  are 
trussed,  and  are  then  termed 
trussed  girders.  Kule  to  determine 
the  transverse  strength  of,  23-i. 

Glaxier.  —  An  artizan  that  per- 
forms the  work  of  fixing  the  glass 
in  windows. 

Glne.— Made  from  the  hide  and  hoof 
of  animals;  the  older  the  animal 
the  better  will  be  the  glue,  102, 103, 
2i6. 

Griflin.  —  A  nondescript  animal, 
used  in  the  sculptured  decorations 
of  the  ancients. 

GriudHtone. — Rule  to  calculate 
the  weight  of,  241.  To  true-up  a 
grindstone  use  a  piece  of  gas-pipe. 

Groin. — A  line  traced  through  the 
intersection  of  two  arches,  termed 
the  line  of  curved  hip  or  groin.  To 
find  the  length  of  and  cuts,  231, 232. 

Groove. — A  sunken  rectangular 
channel. 

Ground  Floor.— The  floor  level 
with  or  first  above  the  curbstone, 
or  roadway;   the   same   may   be 


yt 


Glossaf.y  And  Ixpex. 


termed  the  groiind   plan  of  the 
house. 

Grousids— Are  narrow  strips  about 
2V2"  wide  and  ?s"  thick  nailed  up 
straigrht,  true  and  plumb  around 
all  doors,  windows  and  walls,  as  a 
Kuide  for  the  plasterer,  and  also 
for  nailing  up  the  finish. 

Gront.— Is  composed  of  quick-lime 
and  fine  sand  thinned  down  to  the 
consistency  of  cream  and  poured 
into  the  joints  of  masonrj'.  In 
brick  work  it  is  applied  every 
sixth  course  under  each  heading 
course,  and  every  course  in  stone 
woi'k  to  fill  up  the  cavities. 

Gnill«clie.--A  string  ornament  in 
the  form  of  a  series  of  circles  in- 
terlacing each  other;  a  style  of 
fret,  or  hasl;et  u^nrk. 

Giirg-oil.— A  water  spout  project- 
ing from  a  roof  gutter  to  carry  the 
water  from  the  walls ;  it  is  some- 
times carved  into  a  grotesque  head 
or  animal,  the  water  issuing  from 
an  open  mouth. 

Gnttae. — Ornaments  of  conic  form 
on  the  cornice  of  ihe  Doric  order; 
they  are  supposed  to  represent 
drops  of  water.— LS/i(art. 

Gypsum. -Sulphate  of  lime  21  per 
cent,  water;  when  subjected  to  a 
moderate  heat  the  water  is  with 
drawn,  and  plaster  of  paris  is  the 
result. 

Hall.— That  part  of  a  house  in 
which  the  stairs  are  situated  is 
termed  the  stair  hall. 

Hnlf  Pace.— The  level  platform 
between  two  parallel  flights  of 
stairs.    See  quarter  pace. 

IBalfRonnii.— A  moulding  that  is 
semicircular  in  form,  simihir  to  a 
bead  or  torus. 

Ilainnicr  Beasn.— A  short  hori- 
zontal beam  in  the  hammer  hcam 
truxfi,  common  in  Gothic  roofs. 

Hand  Rail  of  a  Stairr.-»se.— A 
piece  of  wood  smoothed  and  neatly 
moulded,  set  on  balusters  for  a 
grip  to  assist  one  in  ascending  and 
descending  a  flight  of  stairs,  and 
also  to  protect  one  from  falling 
down  the  well  hole;  straight  part 
of,  210;  to  straighten  the  crooked 
part  of,  115.  210;  cutting  and  joint- 
ing the,  115,  149,  174,184;  hanging 
and  preparing  for  the  balusters, 
115,  ITS;  taking  the  lengths  for 
jointing,  107,103;  profiles  of  hand- 
rails, 210;  scraper,  98;  boring  tlie 
rail,  175, 209 ;  to  stain  the  sap  wood, 
210;  building  up  straight  rail,  210. 

Haniicbes  of  an  Areli. —That 
portion  of  an  arch  between  the 
keystone  and  the  springing  stxine 

Header.- In  carpentry,  the  double 
joist  into  which  the  tail  joist  are 
framed.  In  masonry,  the  sfone 
that  extends  through  the  tliick- 
ness  of  wall;  they  are  also  termed 
bimd  or  through  sitonea.  In  brick 
work,  where  the  brick  is  laid 
lengthways  across  the  thickness  of 
wall,  it  is  termed  a  heading,  or  bond 
course. 

Sead- Way.  —  The  space  allowed 
between  a  flight  of  stairs  and  the 
joist  of  the  next  floor  above.    How 


to  calculate  for  trimming,  100, 11? 
148, 177. 

Heel  of  a  Rafter.— That  part  of 
the  rafter  that  buts  the  rawuiflf  or 
pole  plate  to  receive  the  thi-ust  of 
rafter. 

Helical  T<iiie  of  a  Hand  Rail. 
—The  spiral  line  twisting  around 
the  cylindric  section,  forming  the 
twist  of  hand-rail  for  squaring  up 
the  wreath-piece,  readj*  for  mould- 
ing, 41. 

Helix.— A  small  volute  or  twist 
under  the  abacus  of  the  Corinthian 
capital;  in  every  perfect  capital 
there  are  sixteen  helices,  two  at 
each  angle  and  two  meeting  under 
the  middle  of  each  face  of  the  aba- 
cus. 

Heptagon.- 22. 

Hexajfon.- 22 

Hip  Knob.— A  pinnacle  placed  at 
the  apex  of  a  hip  roof;  wrongly 
applied  to  the  barge  terminal  at 
the  summit  of  a  gable. 

Hip  Rafter.— The  angle  rafter  in 
the  inclined  i-idge  formed  by  the 
jack-rafters  of  a  hip  roof.  To  flind 
the  length  when  the  angle  on  plan 
is  aright  angle,  214,  212,  213;  to  set 
a  gauge  for  V)acking  the,  217 ;  to  find 
the  cut  against  the  ridge  plate  af- 
ter the  backing  is  done,  315 ;  to  find 
the  length  of  hip  when  the  angle 
on  plan  is  either  acute  or  obtuse, 
216;  to  find  the  cut  against  the 
ridge  plate  before  the  backing  is 
done,  217;  to  find  the  backing  for 
a  hip,  217,  213;  to  find  the  bevels 
for  hip  framing  of  rafters,  213. 

Hig-lit  or  Height.— Either  is  cor- 
rect.-[TT'ctefe?-.!  The  perpendic- 
ular hight  of  anything  above  its 
base  or  foundation. 

If  istory  of  Stair-Bnilding.— 9, 
20. 

Hoarding.- The  timber  enclosure 
about  a  building  during  erection 
or  repairing. 

Hod.— For  plasterers,  241;  for  brick- 
layers, 239. 

Hold-Fast.-  A  hook  to  drive  into 
^he  wall  to  which  a  wall-rail  is  se- 
cured, 95. 

Hollow  Newel  Stair-Case.— An 
open  staircase  in  contradistinction 
to  a  solid  newel,  into  which  the 
steps  are  secured  and  supported. 

Horizontal  Line.— 21. 

Hood.  — A  projecting  cornice  or 
roof  over  an  outside  opening  to 
turn  the  rain  or  snow;  usually 
held  in  place  by  a  bracket  on  each 
side  of  the  aperture. 

Hood-  WonUIinjf.— A  projecting 
moulding  over  an  outside  door  or 
window  as  a  projection  to  the  fin- 
ish from  the  weather;  also  termed 
drip-moulding,  label  or  weather 
moulding. 

Honsing:.  —  An  excavation  in  a 
stair  string  into  which  is  fit  the 
steps  and  risers,  91,  94;  pattern,  95. 

Hyperbola.— 30. 

Horseing-'l'p  Stairs.— A  term 
used  by  stair-builders  for  support- 
ing a  flight  of  stairs;  iron  rods 
used  for  support,  128 ;  to  construct 
a  truss  bearer,  129;  how  to  cut 
rough  brackets,  128;  the  use  of 


Glossary  axd  Ixdex. 


XI 


scantling  and  brackets,  .30;  sup- 
portiuK  winders  underneath,  KiO; 
self-supixjrting- stairs,  303;  using  a 
Hitched  horse,  131;  thickness  of 
iron  flitch  in  proportion  to  the 
wood,  131. 

Impost.— The  upper   stone    in   a 

-  pier  or  pilaster  from  which  the 
arch  springs.  When  moulded 
forming  a  cap  or  capital,  it  is  term- 
ed the  imiMM  moukliw.h 

Inclination.— A  line  that  inclines 
oblique  to  another  that  is  horizon- 
tal, and  if  continued  will  inter- 
sect. 

Incliue<l  Plane.  —  One  that  is 
oblique  to  a  horizontal  plane. 

Indetinite.- Not  limited  as  to  dis- 
tance. 

Internal  An$rle.— 22. 

Inverted  Arch.— An  arch  with 
the  crown  turned  down;  some- 
times used  under  piers,  columns 
or  walls  in  compressible  soil  to 
distribute  the  weight;  they  should, 
however,  be  used  with  caution,  as 
they  may  do  more  harm  than  good. 

Iron.— To  find  the  weight  of,  see 
Table  10. 

Isoinetrical  Projection.  —  The 
principal  of  hand-railing  illus- 
trated by  prismatic  solids,  38,  43, 
48 

Isosceles  Triangle.— 23;  to  find 
the  area,  23. 

Jacli- Arch.— An  arch  one  brick  in 
thickness. 

Jack-R»fter.— In  a  hip  roof  each 
rafter  that  is  shorter  than  the 
common  rafter  is  termed  a  jack- 
rafter.  To  find  the  length  of,  213; 
to  find  the  bevels  for  the,  213,  217; 
a  short  method  to  line  oft  the,  217; 
each  length  given  on  the  common 
rafter,  216;  the  different  lengths 
given  between  the  hip  and  valley 
rafter,  214. 

Jack-Ril».— The  rib  supporting  the 
groin  or  angle  rib;  how  to  find 
their  different  lengths,  curves  and 
cuts  for  the  same.  221,  222, 

Jambs.— The  vertical  sides  of  any 
aperture,  such  as  a  door,  window 
or  chimney 

Jaml>  fyining^s.— The  wood  work 
to  which  the  door  is  hung,  and  the 
inside  finish  is  nailed. 

Jamb  Stones.— The  stones  form- 
ing the  openings  in  walls  for  doors 
and  windows;  every  other  stone 
should  cross  and  finish  through 
the  entire  thickness  of  wall,  and 
never  built  on  their  edge. 

Jerken-IIeatl.- A  truncated  ga- 
ble. 

Jib  Door.— A  secret  door  that 
stands  flush  with  the  wall,  without 
any  projecting  mouldings,  having 
the  base  and  surface  carried  across 
for  concealment. 

Jogrg-le.- A  projection  in  a  joint  to 
prevent  its  sliding;  the  joints  of  a 
straight  arch  are  sometimes  cut 
with  a  joggle  for  that  purpose. 

Joinery.— The  art  or  practice  of 
preparing  and  fixing  woodwork 
for  the  inside  and  outside  finish- 
ings of  houses,  212. 

Joint.— The  abutting  of  two  pieces 
forming  either  a  dose  or  open  joint. 


A  clean  close  joint  is  the  pride  of 
a  joiQcr. 

Joist.— The  timber  to  which  the 
flooi'ing  boards,  lath  or  stripping 
for  lath  are  nailed.  Formula  to 
calculate  their  transverse  streng-th 
224;  stiffness  to  prevent  the  crack- 
ing of  plaster,  129. 

Kerf.— The  cut  made  by  a  saw;  sys- 
tem of  bending  by  kerfing,  155. 

Key.— Pieces  of  wood  cut  and  fit 
and  glued  into  grooves  when  bend- 
ing a  cii'cular  stair  string  over  a 
drum  to  hold  the  string  to  the  re- 
quired curve,  are  termed  keyri. 
Foldinri  lii^ys  are  used  to  fasten  the 
newel  post  to  the  floor;  also  to 
draw  the  veneer  close  to  the  block 
in  a  curtail  step;  also  used  in 
scarfing  to  draw  the  joint  close. 

Keystone.— The  highest  and  mid- 
dle stone  in  an  arch.  Sometimes 
the  keystone  is  allowed  to  project 
from  the  face  of  arch  and  is  mould- 
ed and  carved. 

Knee.— That  part  of  a  hand-rail 
connecting  the  newel  at  a  land- 
ing with  the  ramp  is  termed  a 
rcunp  and  knee,  or  goose-neck.  All 
straight  casings  of  a  hand-rail  that 
are  concave  on  the  back  are  term- 
ed ramps;  and  those  that  are  con- 
vex are  termed  knees. 

King-Post.— Or  king-bolt,  thecen- 
ter  post,  or  bolt  in  a  roof  truss; 
when  used  the  truss  is  termed  a 
king-post  or  king-bolt  truss. 

Isabel. —In  Gothic  architecture,  the 
drip  or  hood  mouldinij  of  an  arch 
when  it  is  returned  square.— i>7it- 
art. 

K<a8:g-iii;sr-  —  Strips  nailed  across 
ribs,  forming  centers,  to  carry  the 
arch  stones  or  brick  work,  or  to 
increase  the  diameter  of  wooden 
pulleys. 

I^anding-.— The  floor  at  the  head  of 
a  flight  of  steps,  or  any  rest  be- 
tween flights. 

I.andiug'  Step.— The  last  step  in  a 
flight  of  stairs  which  connects  the 
floor  at  the  landing  or  any  resting 
place. 

I<autern.— A  turret,  either  square, 
IKjligonal.  circular,  or  elliptical, 
placed  above  a  dome  or  tower. 

tanndrj'.  —  The  apartment  in  a 
dwelling  arranged  for  the  washing 
and  drying  of  the  clothes  for  the 
family. 

Iia%'at-ory.— A  small  room  provided 
with  washstand  for  washing  the 
hands  and  face. 

Ledge.  —  The  projection  against 
which  the  door  closes.  A  very 
narrow  shelf. 

Ledger.- In  scaffolding,  the  hori- 
zontal boards  nailed  to  the  stand- 
ard.'<  or  uprights  to  support  one  end 
of  the  put-loqs  on  which  the  boards 
are  placed  for  the  AS'orking  plat- 
form. 

Length.— The  greatest  extension 
of  a  body. 

Level.— Horizontal;  water  when  at 
rest  is  level. 

Lewris.— A  devise  to  insert  in  a 
dovetail  mortise;  used  in  lifting 
heavy  stone  with  the  gin,  derrick, 
crane  or  any  hoisting  apparatus. 


XII 


Glossary  and  Iitdex. 


I<ibrary.  —  The  dopartment  or 
building'  provided  with  cases  for 
the  reception  of  books. 

Ijime.  -By  exposiug'  limestone  to  a 
red  heat  the  cai-bonic  acid  is  ex- 
pelled; the  result  is  qitich-lime; 
then  if  -water  be  applied,  it  is 
termed  a  hydrate  of  lime,  or. ■'lacked 
Jime,  21. 

Iilning'Ont. — The  lining  or  mark- 
ing out  of  patterns  and  stuff  re- 
quired by  the  carpenter  or  joiner 
to  be  cut  into  smaller  pieces. 

liinitig-s.— Door  jambs  and  back 
linings,  panel  backs  and  elbows 
for  inside  shutters,  the  woodwork 
around  doors,  windows,  or  the  cov- 
ering- of  wall  as  wainscoating,  sof- 
fits, &c.,  for  the  interior  finish  of  a 
building;  for  the  exterior,  it  is 
termed  casing. 

Hjjf  el.— The  horizontal  timber  or 
stone  over  au  opening  for  a  win- 
dow or  door  to  curry  the  super- 
incumbent weight  to  the  supports. 

I..oam.— A  mixture  of  fine  sand  and 
clay;  a  little  is  sometimes  used  by 
the  plasterer  to  make  the  mortar 
-work  easy. 

I>oJ>l».v.— An  enclosed  space  from 
which  entrance  is  made  into  one 
or  more  apartments. 

I^o^sif*  —An  open  space  recessed 
in  a  wall  from  which  to  obtain  a 
view  of  the  surroundings. 

I.nflrer,  or  I-osiver- Boards.— 
Boards  set  inclining  in  an  aperture 
and  spaced  so  as  t()  admii  air  and 
exclude  rain;  used  in  bell  towers, 
stables,  factories,  to  carrj-  oS  the 
smoke  and  allow  a  free  circulation 
of  air, 

I^ozftsige.— A  quadrilateral,  23. 

I^of t.— A  room  in  the  I'oof  of  a  build- 
ing; a  gallery  or  small  chamber 
raised  within  a  larger  apartment, 
or  in  a  church,  as  a  music  loft,  a 
singing  loft,  a  rood  loft,  &c.— Par- 
1;cr. 

Mahoffany.  —  A  wood  sometimes 
used  for  doors,  sash  and  hand  rails 
of  stairs;  the  best  quality  comes 
from  the  mountains  of  .Jamaica, 
that  which  comes  from  Honduras 
being  soft  and  often  spongy;  it 
should  be  air  dried  and  not  forced. 
The  genuine  San  Domingo  mahog- 
any is  easily  identified  by  the  pores 
being  filled  with  a  white  substance 
resembling  flour.  The  Mexican 
mahogany  is  better  than  the  Hon- 
duras. 

M«*an.— In  mathematics,  the  aver- 
age of  the  sum  of  all  the  quanti- 
ties. 

Measiire.—That  by  which  extent 
or  dimension  is  ascertained;  table 
of  board,  242.  243. 

]tle<-haiiicHl    Carpentry.  —  212. 

>!i«!ia»-«'al   Arcliiloclnro.  —  The 

architecture  of  Eugland,  France, 
Germany  and  Italy  during  the 
middle  ages,  including  the  Nor- 
man and  early  Gothic  styles,  from 
A.  D.  4fX)  to  1500. 
ullcdallion.— An  oval,  circular  or 
sometimes  square  tablet,  on  which 
are  embossed  figures,  busts  and 
the  like. 


Moinher.  —  Different  parts  of  a 
moulding,  or  the  separate  parts  of 
a  cornice,  entablature  or  column, 
as  the  base,  fillet,  torus,  conge,  or 
capital. 

2H[«>tev — The  French  unit  of  length, 
231. 

Mezzanine  Story.— Two  stories 
within  the  height  of  one  story, 
mostly  divided  at  the  platform  of  a 
stairway ;  it  is  also  termed  the  en- 
tresol story. 

Mixtilinear.— Angle,  21. 

5Io«li31ioii.— A  cornice  ornament 
similar  to  a  bracket,  having  a 
greater  projection  than  height. 

Monkey.  —  Used  as  a  weight  in 
driving  piles  ;  fi-om  its  weight 
and  force  to  ascertain  the  stabil- 
ity of  a  di-iven  pile,  23S. 

Mortar.— A  mixture  of  lime  and 
sand  used  to  cement  stone  and 
brick  in  a  wall  and  plaster  in  a 
building;  is  composed  of  two-thirds 
clean  river  sand  and  one-third  well 
burnt  lime.  Hydraulic  mortar  is 
made  from  cement,  and  used  in 
the  construction  of  piers  or  walls 
under  water,  as  it  soon  hardens  by 
the  action  of  the  water. 

Mortise-  --  A  rectangular  hollow 
made  in  a  timber  with  auger  and 
chisel,  into  which  is  ^:t  a  tenon 
made  on  the  end  of  another  piece 
of  timber.  The  sides  of  the  mor- 
tise are  termed  the  checks. 

JloiiUiings.  —  The  ornamental 
forms  applied  to  the  projecting 
and  receding  members  of  an  order. 
The  contour  of  the  Grecian  mould- 
ings have  a  curve  of  a  conic  sec- 
tion; the  Roman  form  of  the 
moulding  was  arcs  of  the  true  cir- 
cle. In  the  five  orders  thei-e  are 
but  eight  regular  mouldings,  the 
(ivolo,  the  Tcdou.  the  Cyma,  the 
Cavetto,  the  Torus,  the  Astraf/nl, 
the  Scotia  and  the  FiUct.  The  pro- 
jection of  a  moulding  is  about 
eijual  to  its  height  as  a  rule. 

Mnilion  -  Franse.  —  A  window 
frame  divided  into  two  or  more 
openings  by  vertical  posts.  (See 
window.) 

Mmitin.- The  short  pieces  in  a 
door  that  are  cut  between  the 
rails  are  termed  muntins. 

Net  Measure  Is  such  when  no 
allowance  is  made  for  waste  of 
material. 

Neutral  Axis.— That  plane  in  a 
beam  in  which  the  tensile  and 
compressive  forces  terminate,  and 
therefore  nothing.  227.  22!i,  131. 

Ne-tvel  Post.— In  close  winding 
stairs  the  shaft  around  which  the 
steps  and  risers  wind  at  their  nar- 
row ends.  In  open  slaii's  the  post 
at  the  starting  is  termed  the  vc.wcl 
pout;  if  posts  be  placed  at  the 
angles  insteacl  of  cylinders,  they 
are  termed  annlc  ncvils;  box  or 
built,  211;  solid,  152;  standard 
lengths,  152. 

Xirhe.— A  recess  in  a  wall  for  the 
reception  of  a  statue,  vase  or  other 
ornament;  they  were  a  decorative 
feature  and  much  used  in  the  mid- 
dle ages.  178. 


Glossary  axb  I^dex. 


xiu 


Wouason.— 22. 

BTornial  liine.  —  In  geometry  a 
line  drawn  perpendicular  to  any 
line  is  normal  to  that  line.  To  find 
the  normal  line  anywhere  in  the 
elliptic  curve,  31. 

No«iing'  of  Steps.— The  projecting 
moulding  on  the  edge  of  a  step,  92, 

Oblonff.— A  rectangle  of  unequal 
dimensions. 

Obtnse  Anjfie-Triaiigle.— 21. 

Octagon. -To  draw,  27. 

Open  Strinsf.— An  outer  string, 
finished  with  return  nosings  and 
brackets,  the  balusters  being  dove- 
tailed into  the  steps. 

Orders.— There  are  five  ordei-s.  the 
Tuscan,  Doric,  Ionic,  Corinthian 
and  Composite.  Each  have  their 
ornaments;  and  the  understand- 
ing and  application  of  which,  con- 
stitutes the  foundation  of  all  ex- 
cellence in  the  art  of  architecture. 

-IGwUt. 

Out  to  Ont.— Any  dimension  taken 
to  its  utmost  bounds. 

Outer  Strinsr.— The  front  or  face 
string  bounding  the  well  hole  of 
the  staircase,  if  trimmed  witli 
bracket  and  return  nosings,  is 
termed  an  open  t<tiiii(j;  if  jjaneled 
and  steps  housed  in  on  the  back,  it 
is  termed  a  close  stri)i(j. 

Ont  of  Winrtinj;.— A  surface  per- 
fect! j'  straight  and  true  every  way. 

Oval.— 33. 

Ovolo.  —  A  convex  moulding  re- 
sembling a  (fiiartcr  round,  us  the 
Koman  echinus.  In  the  Grecian 
arcliitecturc,  the  ovolo  is  elliptical 
or  egg  shaped. 

l»aco.— The  landing  in  a  staircase. 

I»»ne3.— A  thin  lioard  having  all  its 
edges  inserted  in  the  groove  of  a 
surrounding  frame,  as  the  panels 
of  doors,  shutters,  &o.  In  mason- 
ry, it  is  one  of  the  faces  of  a  hewn 
stone. 

I'asntiii;?.  The  flist  coat  in  paint- 
ing consisting  of  linseed  oil,  tur- 
pentine and  white  lead  is  mixed 
thin  so  that  tho  wood  will  absorb 
the  material;  it  is  termed  the 
pritni)i'.i  coat.  A  coat  of  paint 
made  of  white  lead  and  turpentine 
leaves  no  glo.ss,  and  is  termed  ^at- 
lin<i. 

I'arsspet.  — A  wall  about  four  feet 
high,  built  of  any  materi*!,  as  at 
the  entrance  of  a  bridge  or  on  a 
terrace,  or  cornice  of  a  building 
for  protection. 

S»ara!l»ola.    30;  parabolic  curve,  30. 

l»arj»lSol  IjineN.— 21. 

ParaSlelosr «•»«».  -32, 

Pars'ct.  This  term  is  applied  to 
the  plaster  used  in  lining  the  tlue 
of  a  ciiiinney,  formed  of  lime, 
mor!;:u-  and  cows'  dang.—Gwilt 

I»j»Yi«lioii.  —  A  turret  or  small 
building,  generally  insulated,  and 
compristid  under  a  single  roof,  as  a 
nummrr  house, plcdstire  /loitse,  &c. 

Pedestal.— In  the  classic  orderfl, 
the  lowest  division  in  an  order  of 
columns;  it  consists  of  three  prin- 
cipal parts,  the  iM-fC,  the  die  and 
the  cornice,  on  which  the  plinth  of 
ttie  column  rests.  When  the  pe- 
destal is  continuous,  supporting  a 


range  of  columns,  it  is  termed  a 
podium  or  stylohate. 

Pediment.  —  In  classic  architec- 
ture the  triangular  finish  over  a 
portico.  In  the  architecture  of  the 
middle  ages  small  gables  over 
openings  were  termed  pediments, 
the  angle  at  the  apex  being  often 
acute  instead  of  obtuse,  as  in  the 
classic. 

Penttentive.— An  arched  or  vault- 
ed ceiling  drooping  at  the  angles 
and  forming  arches  on  the  plane 
of  the  walls.  Pendentives  are 
sometimes  either  spherical,  elliyj- 
soidal  or  conical.  The  apartment 
may  be  either  square,  oblong  or 
polygonal. 

Pen  tag-OSS . —22 

PercSi.— A  measure  of  stonework, 
231-238. 

Perpeaidicular.— 21. 

Piaxza. — An  open  space  surround- 
ed by  buildings  or  colonades. 

Pier.— A  solid  between  openiugs,a,5 
the  space  between  windows  and 
doors;  the  solid  structure  from 
which  two  arches  spring  in  a 
bridge,  the  shai-e  end  being  the 
abutment. 

Pilasjer.— A  square  column  pro- 
jecting from  a  wall  one-fourth  or 
oue-flfth  its  breadth. 

Pinnacle.— The  top  finish  to  a  but- 
tress or  gable;  the  apex. 

Pj!e  —A  large  timber  pointed  at 
one  end  and  driven  into  the 
ground  on  which  the  foundation 
of  a,  structure  is  commenced,  ajs. 

Pitcli-Board.— A  right  angle  tri- 
angle made  from  a  thin  board  of 
hard  wood  to  suit  the  rise  and 
tread  of  a  stairs,  and  used  to  la.v 
otf  the  strings,  9U;  stretch  of 
pitch-board,  95,  90. 

Plan.— A  draught  showing  thehorl- 
zonlal  section  of  a  building,  or  any 
part  thereof. 

Planceer.  —  The  horizontal  pro- 
jecting members  of  a  cornice;  the 
raodilions  arc  secured  to  its  sofiit. 

Plane.— In  geometry  a  true  sur- 
face. 

Plaster- IVorlc.— The  application 
of  plaster  to  walls  and  ceilings. 

Plasterers.— McMiioranda,  2VI, 

Plastering-.  —  The  first  coat  of 
plaster  on  lath  is  termed  priekiwj 
up,  or  Kcnilch  coat;  if  on  brick 
v.'alls  it  is  termed  )-enderiiig;  the 
mortar  is  termed  coar.se  stulf;  if 
allowed  to  become  too  dry  before 
the  second  coat  is  put  on,  the  sec- 
ond coar  is  apt  to  droiJOIT;  hence 
for  good  work  it  is  considered  be.-t 
to  put  on  the  seond  coat,  termed 
the  '/'».((('H!/por(t,  when  the  Ui-stcoat 
is  about  half  drj",  and  t<liim  when 
the  plaster  is  dry;  this  is  termed 
thrcc-cmt  tvorl;.  Floa'Auij  srrcciis 
are  strips  of  plaster  set  out  ver- 
tically every  three  or  four  feet  or 
more  as  a  gauge,  and  to  suit  the 
length  of  the  f.i>ct-.-ndc.  The  float- 
rule  is  of  various  lengths;  wnon 
very  long  two  men  are  required  to 
handle  it;  with  the  tloat-rule  or 
iitraiiilit  cd<jo  plaster  is  put  ou  a 
wall  to  a  true  surface.  For  run- 
ning stucco  cornice  the   screeds 


XIV 


Glossaky  and  Index, 


are  horizontal  and  made  of  wood. 
Lime  slacked,  sifted  aad  mixed  to 
a  thickness  of  cream,  then  allowed 
to  evaporate,  forming'  a  paste,  is 
termed  flue  stuff  or  puttii;  it  is  used 
for  the  last  coat,  or  ,s7f i/(i-coaf,af  ler 
the  lloatod  coat  is  dry  or  nearij- 
so.  When  flae  stuff  is  mixed  with 
plaster  paris  and  a  little  white 
sand  to  form  a  hard  surface  at  the 
corners,  jambs,  walls  or  running' 
mouldin!?s,  it  is  termed  (jauijiil 
stuff.  A  half  peck  of  white  sand  is 
allowed  to  a  bushel  of  fine  stuff 
for  skimmiug;  and  for  gauged 
work  allow  two  quarts  additional 
of  plaster  paris. 
Point.— 21. 

Posiiioii. -In  geometry  the  situa- 
tion of  one  thing  in  regard  to 
another.  IStuart. 
Post.  .  A  timber  set  upright  as  a 
support,  termed  a.  corner  pnxt  in  a 
house,  /f i»i{/  or  queen  post  in  a  roof, 
newel  post  in  stair-case;  a  (late  or 
fence  post;  also  a  support  to  floors 
in  warehouses  and  other  struc- 
tures. To  calculate  the  strength 
of.  328;  regard  to  its  position  for 
safety,  238;  increased  strain  when 
inclining,  228,  229. 
Pi-iiicipal    Rafter.  ..  See    truss 

roof. 
Problem.  .-In  geometry  a  proposi- 
tion iu  which  some  construction  is 
reo.uired. 
Pro«lnccd  ...Extended  in  length. 
Profile..   In  architecture,  the  con- 
tour of  a  mou. ding  or  mouldings, 
or  the  outline  of  a  cross-section  of 
a  building,  or  any  piece  of  work. 
Prolonged.  .  Continued  in  length. 
I'roNcenlHni    Arch.  ...  An    arch 
over  the  stage,  back  of  which  the 
curtain  drops. 
Pulley. ...Speeding  pulleys,  24.5. 
Purlin...  A  horizontal  i>ieceof  tim- 
ber in  a  truss  roof  resting  on  the 
principal  rafters  and    snpiiortiug 
the  common  rafters  and  their  load 
To  find   the  cuts  against  the  hip 
rafter,  211.  213. 
QnadruKglc.  .  .  Any    figure  with 

four  angles  and  four  sides.  22. 
<jHa«lrant...  The  <iuarter  of  a  cir- 
cle  2t. 
<tua<lrilateral.    22. 
Q,nMrter-j»«ce... A  landing    in   a 
stair  case,  wlieie  a  per.son  going 
either   uj)  or  down,   makes    one 
right  angle    turn;    if  two  right 
an.gle  turns  on  the  same  pace,  it 
is  termed  a  lialf-piicc. 
«6iiarler  Kawe«l..    Lumber  that  is 
sawed  fro:n  the  log  on    the  nicdu- 
lary  rays  is  termed  (juarter  sawed 
lumber. 
«ti»eeii-Post    Itoof     A     roof    in 
which  a  straining  beam  jiiid  two 
posts  or  bolts  are  used  instead  of 
one  as  in  th<?  king-post  roof. 
4luirk-9l4»ul<liiiK'.      A   moulding 
showing  a  d<>ei)    narrow  channel 
at  its  greatest  projection  to   ob- 
scure the  joint. 
Kadial   f^inex.    Lines  projec*^ing 
in  different  directions  from  a  com- 
mon center;  also  termed  convery- 
hm  lines. 
Kadi  us,    24. 


Rafter, ...The  inclining  timber  in  a 
roof   on  which    the    sheathing  is 
nailed:  to  find  the  length  of  com- 
mon 213,  21.5,  216;    to  find  the  cuts, 
213,  217, 
Rake.    An  inclination  or  slope,  as 
the  pitch  of   a  stair  case  or  roof, 
or  anything  that  inclines    to  the 
horizon. 
Ramp...  A  concave  bend  rising  up. 
(See  knee)  to  locate  the  points  on 
pattern  for  jointing  the  rail,  lOB. 
Raising'- Plate.    .  The    board    se- 
cured to  the  ends  of  the  ceiling 
joist  to  receive  the  heel  of  rafters. 
Rail.  ..In  joinery  framing,  the  hor- 
izontal pieces  in  doors,  sash,  shut- 
ters or  wainscoating. 
Rebate...  A     rectilineal      channel 
worked  on  the  edge  of  a  piece  of 
stuff. 
Rectangle.  ..A  figure    whose   an- 
gles are  all  right  angles ;  22. 
Rectilinear.    A     figure      whose 

boundaries  are  right  lines. 
Relieving  Arcli.  ..An  arch  built 
over  a  stone  or  wood  lintel,  or  over 
a  flat  arch,  to  carrj'  the  load  to  the 
pier. 
Retaining  Wall... A  heavy  strong 
wall  constructed  with  a  batter  to 
prevent    a    bank    of  earth    from 
sliding  down. 
Rhomboid.    A  quadrilateral;  22. 
Rhombus.. .22. 

Reveal.    A   rectilineal    rebate   or 
recess  at  the  sides  of  an  opening 
for  a  door  or  window  between  the 
frame  and  the  face  of  wall. 
Ri'b   ..A  curved  timber,  forming  an 
arch,  to  which  the  lath  are  nailed; 
221. 
Ri«lge.    The  comb  or  highest  part 
of  a  roof,  where  a  pair  of  rafters 
butt  the  riiige  }jlate. 
Right  Angle.    An  angle  contain- 
ing 90  degrees;  22,  21. 
Right    iJne.    A   line    absolutely 

straight;  21. 
Rise.   .One  of   the   divisions    Info 
which  the  height  of  a  story  is  di- 
vided for  a  stair-case:  'JO. 
Riser.    The  vertical  board  between 

two  steps. 
Sand.    Proportion  to  lime  in  mor- 
tar, 241. 
Sash.    The  frame  holding  the  glass 

in  :i  window 
Scalfolfl..   An  assemblage  of  scant- 
ling,  planks  or  boards  erected  to 
support  workmen  in  the  construc- 
tion of  a  building. 
Scalene  Triangle.    23. 
Scarfing.    The    splicing    of     two 
pieces   of  timber    together  to  in- 
crease their  length. 
Scotia.  —  A    cove    inoulding,    the 
contour  of  which  is  a  (juarter  cir- 
(de  or  a  quarter  ellipsis. 
Scribing.— The  fitting  up  of  any 
piece  of  woi'l;  to  an  uneven  sur- 
face with  the  dividers. 
Scroll.— A   name    given   to  spiral 
ornaments,   as    the    termination 
sometimes  given  to  a  hand-rail 
at  its  starting,  and  al.so  the  vo- 
lutes of  the  I(>inf  and  t'orinthian 
capitals.  When  a  hand-rail  starts 
with  a  wreatlK-d  .scroll  the  first 
step  is  termed  the  scroll  or  curtail 


GLOSbAiiv  a:si)  1^.UEX. 


XV 


step.  When  a  hand-rail  starts 
from  a  newel  with  a  straight 
easement  worlved  into  a  scroll  on 
top  of  the  newel,  it  is  termed  a 
ccrtical  scroll.  Hov/  to  draw,  '65; 
reciprocal  scroll  to  draw,  35: 
how  the  eye  may  be  formed  to 
I  he  best  advantage,  309. 

Seasoned  'I'iinber.  —  Such  as 
rendered  sufficiently  dry  to  be 
used  for  the  rough  framing  tim- 
ber. 

Sectionof  a  Bnildin^.— A  ver- 
tical plane  or  planes  through  any 
portion  of  a  structure  represent- 
ing the  walls,  doors,  windows, 
flues  and  finish  on  that  particular 
plane. 

Segiiieiit— 24. 

Se«ni-€ircle.    24. 

Self-Knpportiiigr  Stairs.  ...  203; 
mode  of  construction,  203. 

Shalt.. ..The  body  of  a  column  be- 
tween the  base  and  the  capital. 

Sbakey  I^tiiiiber. ..That  in  which 
the  growths  or  annual  rings  are 
disunited  by  the  action  of  winds 
and  frost. 

Sbaiik  of  a  M'reHtta-Piece... 
The  straight  part. 

Sliearingf.... Strength  of  timber 
per  square  inch,  Table  7. 

Suingles... .Number  to  the  square, 

Shoe. ...The  inclined  piece  at  the 
foot  of  a  conductor  to  turn  the 
water  from  the  building-;  if  long 
and  cast  of  metal  it  is  termed  a 
boot;  also  an  iron  socket  at  the 
foot  of  a  rafter  or  strut  to  re- 
ceive the  thrust. 

Shiifters.  .An  appliance  to  shut 
out  the  light  from  a  window. 

Sin^^Ie  or  IJonblw  Worked 
Uoor.... Means  that  the  door  is 
either  moulded  on  one  or  both 
sides. 

Skew- Back.  ...  In  curved  or 
straight  arches,  the  abutment 
that  slopes  to  receive  the  end  of 
an  arch. 

Soffit..  The  ceiling  or  underside 
of  a  stair-case  or  archway,  cor- 
nice or  entablature. 

S|»aiidril....Tlie  triangular  panel- 
ing under  a  flight  of  stairs  is 
termed  a  upaiidrU. 

S|»lay.  ./rhe  term  is  applied  to 
whatever  hasone  side  oblique  to 
the  otlier,  as  the  v/alls  or  linings 
around  doors  or  windows  are 
sometimes  splayed  to  admit  light. 
Bevels  for  splayed  woi-l<,  218;  to 
lind  the  veneer  for  a  splayed  cir- 
cular door-head,  and  also  of  a 
]]ew-back,  220;  to  find  the  veneer 
for  a  circular  door-liead  in  a  cir- 
cular wall,  the  jambs  being  par- 
allel, 220,  221. 

Spring  Bevel.  The  bevel  ap- 
plied to  the  shank  of  a  wreath- 
piece.  Tlie  t)ovel  applied  to  t!ie 
center  .ioint  is  termed  tlie  iiitcli- 
hcvft,  and  l)oth  are  sometimes 
lei-med  the  joinf-hcPKlf. 

S<|ii»re.    To  construct,  2f>. 

Stairs.  A  series  of  steps  leading 
frOTii  one  level  to  another.  The 
horizontal  distance  from  the  face 


of  first  rise  to  the  face  of  the 
rise  landing  is  termed  the  run. 

Stair-Case. ...The  structure  in  a 
building  by  which  communica- 
tion is  made  with  the  ditterent 
stories,  and  includes  all  the 
flights  in  a  well  for  that  stair- 
way. When  of  one  flight,  land- 
ing on  the  ne.xt  floor,  is  termed  a 
level  landiiKj  stair-case;  when  di- 
vided into  two  flights,  running 
parallel  to  each  other,  is  termed 
a  half  pace-stair-ca^e ;  if  winders 
fill  tlie  half  pace,  it  is  then  term- 
ed a  Italf  pace  ivinding  stair-case; 
if  winders  fill  a  quarter  pace,  it 
is  termed  a  quarter  pace  ivindiug 
stair-case;  if  winding  in  two  quar- 
ter paces,  it  is  termed  a  double 
quarterpaceiviitdiv()stai7--casc;il  all 
the  steps  arc  winding  and  circu- 
lar on  plan,  it  is  termed  a  cireu- 
lar  (leomctrical  stair  case;  if  the 
plan  be  an  ellipsis,  it  is  termed 
an  elliptical  stair-cnse;  when  stairs 
are  supported  only  at  the  start- 
ing and  landing,  the  sides  being 
free,  they  are  termed  self-support- 
iiifj  stairs.  To  construct  box,  5)9, 
01,92;  to  line  off  the  string  for 
bo.x,  90;  putting  up  box  stairs,  90: 
preparing  open  stairs,  100, 101, 107, 
108;  setting  up  open  stairs,  lOfi. 
]07,92:to  lineofl  winding  stairs  1.58, 
159, 160, 170; building  self-support- 
ing stairs,  203;  building  elliptical 
stairs.  203;  directions  lor  lining 
oir  strings,  163,  1(54,  165,  178,  179: 
rule  to  proportion  the  step  to 
rise  (Blondel  s),  87, 99 ;  to  construct 
for  a  six-foot  hall,  99;  to  con- 
struct for  a,  two-story  and  seven- 
foot  hall,  116;  flight  outside  steps, 
87;  to  construct  step-ladder,  89; 
to  construct  box  stairs,  90. 

Staves  of  a  t-ylinder.  To  ob- 
tain their  lengths,  102,  165;  man- 
ner of  preparing  theiii  by  ma- 
chinery, 102;  number  to  a  semi- 
circle, 101. 

Stay...  Same  as  brace. 

Step.  A  step  of  a  stair-case  in- 
cludes from  the  face  of  rise  to  the 
verge  of  nosing,  90;  preparing  tiie 
steps,  mitering,  dovetailing  and 
gluing,  128,  104,  Kkj;  graduating 
the  flyers  and  winders,  73;  pat- 
tern for  circular  end  steps,  104, 
108;  gluing  up  Step  and  rise,  105; 
if  crooked,  105;  nosing  the  step, 
105;  mitering  step  for  nosing,  108; 
grooving  and  tongueing,  lOS; 
thickness  to  length  of  step, 80; 
oak  for  outside  steps,  89;  making 
step-ladder,  89;  making  cellar 
steps,  88;  cutting  out  steps,  127. 

Stile..  .In  joinery  the  vertical 
pieces  that  bound  a  piece  of 
framing  and  are  made  ridged  to 
the  horizontal  pieces  by  tenon, 
mortise  and  glue. 

Stirrup  iron.. ..To  calculate  the 
strength  of,  131;  their  value  in 
framing,  227. 

Stereotoniy.  The  science  or  art 
of  cutting  solids  into  certain 
ligures  or  sections,  43. 

Stonemasons..  Riemoianda,  237, 
238;  measuring  stonework,  238. 


XVI 


GLOS.SAKY   AM)   iMtEX. 


Story....Comprehends  the  distance 
from  one  floor  to  that  of  another. 
90. 

Story-Rod.. ..In  stair-building  is 
used  to  measure  off  the  height 
of  story  from  top  of  ^ioist  in  one 
story  to  the  top  of  joist  in  the 
next  preparatory  to  stepping  off 
the  number  of  risers  required;  90. 

Strain..  .A  force  exerted  tending 
to  disarrange  or  destroy  tlie 
structure  or  cohesion  of  any  of 
its  parts.  To  calculate  the  shear- 
ing strain  across  the  grain,  228; 
to  calculate  the  tensile  strain, 
2-30  231;  to  calculate  the  trans- 
verse strain,  224,  225;  to  calculate 
the  compressive  strain,  22;);  to 
calculate  the  stiffness  of  a  post 
or  strut  for  stiffness,  229;  to  And 
the  strain  at  any  point,  227;  to 
find  the  strain  in  a  strut  or  brace, 
229;  to  find  the  size  of  timber  for 
a  given  strain,  227. 

Stretchout....Of  a  semi-circle,  to 
draw,  28. 

String.... In  joinery  that  which 
supports  the  steps  at  lioth  ends; 
that  at  the  wall  side  is  termed 
the  ivall  string;  and  that  at  the 
open  side  or  well  hole  is  termed 
the  front,  or  outer  stritig;  the 
curved  part  is  termed  the  cylin- 
der; tlie  part  that  is  level  and 
lining  the  rough  joist  is  termed 
the  level  string. 

Strut. ...See  brace- 

Stiilf.  .  A  general  term  for  wood 
used  by  joiners. 

Stylo.  ..The  different  classes  of 
arcliitPcture. 

SHb*Plinth.  .A  second  and  lower 
plinth  placed  under  the  principal 
one  in  columns  and  pedestals.— 
INeirUtnds. 

Ta!>l«s..  Table  1,  long  measure, 
2:U;  2,  superficial  measure,  2:jl;  3, 
cuVjic  measure,  231;  4,  avordu- 
poise  measure,  231 ;  7,  resistance 
to  compression,  shearing,  tensile 
and  transverse  strain,  2:j2;  8, 
crushing  sti-cngth  of  building 
material,  Vii;  9,  average  weight 
per  cubic  foot  for  materials  used 
in  the  construction  and  loading 
of  buildings,  233,  231;  10,  weight 
per  lineal  foot  of  .scjuave  and 
round  iron,  234;  II.  to  find  the 
weiglit  of  castings  from  tlieir  pat- 
terns, 23.'»;  12,  the  weiglit  of  vari- 
ous metals  per  superficial  foot, 
235;  13,  weight  per  superficial  foot 
on  roofs  from  various  caiis<;s, 
235;  14,  vertical  reposeof  different 
.soils  for  a  short  time,  23!);  15,  num- 
ber of  cubic  fiiet  to  bo  removed, 
and  nuiiiber  of  briclc  re(|uired 
for  wells  from  3  to  12  feet  in  di- 
ameter, 237;  17,  shows  seven  tests 
of  the  strength  of  brick  piers 
built  in  cement  and  com'mon 
mortar,  WO;  58,  shows  the  thick- 
ness of  walls  for  dwellings  and 
stores  as  .set  forth  in  tlie  building 
laws  of  the  city  of  Chicago,  240; 
19,  materials  required  for  100 
yards  of  plastering-,  three  coats, 
241;  20,  number  of  shingles  and 
rails  per  100  s(|uare  feet,  244;  21, 
showing  the  number  of  nails  re- 


quired for  fixing  1,000  feet  super- 
ficial and  lineal,  244;  22,  approxi- 
mate number  of  cut  and  wire 
nails  to  the  pound,  244;  23,  board 
measure,  242,  243. 

Tail- Joist.. ..Short  joist  tailed  into 
the  header,  as  around  fire-places, 
stairways,  &c. 

Tall-Trimmer.. ..A  trimmer  next 
to  the  wall  into  which  other  joist 
are  framed  to  pass  a  flue. 

Tangent.. ..31,  24. 

TanK.. ..To  calculate  the  pressure 
per  square  inch  of  water  on  the 
sides  and  bottom,  245. 

Tenon.. ..A  projecting  rectangular 
prism  formed  on  the  end  of  a  tim- 
ber to  be  inserted  into  a  cavity 
of  the  same  form. 

Tensile.  -A  strain  tending  to  pull 
apart,  the  strain  being  given  to 
find  size  of  timber  required  for 
safety,  230. 

Thrust.. ..The  force  exerted  by  an 
arch  or  pair  of  rafters. 

Tie-Ream.— The  beam  that  con- 
nects the  foot  of  two  principal 
rafters,  and  neutralizes  the 
thrust  of  same  from  injuring  the 
wall  and  preserving  their  equil- 
librium. 

Tie-Roil. .. An  iron  rod  perform- 
ing the  ofBce  of  a  tie-beam. 

Trammel...  A  device  for  drawing 
the  ellipsis;  to  construct,  33:  sub- 
stitute for,  tjO. 

Transom... A  window  above  a 
door  separated  from  the  door  by 
a  transom  rail,  or  continuation 
of  the  imijo.st  moulding. 

Transver.se..  -Across, at  right  an- 
gles to  the  length;  formula  for 
transverse  strains,  224. 

Tra»e«inm..  .23. 

Trapezoid...  23. 

Tread...  A  t  read  of  a  stair  includes 
the  horizontal  distance  from  face 
of  one  rise  to  the  face  of  next;  or 
the  horizontal  cut  of  the  outer 
string,  90;  rule  to  proportion  the 
tread  to  suit  the  rise,  87. 

Triangle...  22. 

Trimmer... A  double  joist  into 
wliich  a  header  is  framed  to  car- 
ry the  tail  joist,  as  around  the 
lire-place,  stairways  and  sky- 
lights 

Trn.s!*  Roof. .  .Is  composed  of  tie- 
lieam,  inincipal  rafters,  king  or 
queen  bolts  and  struts,  so  ar- 
ranged as  to  carry  tin;  purlins, 
common  rafters,  sheathing  and 
other  weights  to  the  v/alls  which 
support  tliem. 

Turners'  Cement.    24G. 

Twist  lAne  of  a  Ilitnd  Rail. 
The  ln;lix,  or  screw  line  forin.iiig 
the  lAvist  of  a  wi-ealh-piecc,  of  a 
hand  rail,  found  by  lioixling  a 
pliable  strip  around  the  wreath- 
piece  to  agree  with  the  minor 
axis  and  the  axisof  bloi-lc  jjat  tern 
a.s  shown  at  p.  113.  When  there 
are  two  or  more  wreath  pieces 
connecting  each  other,  also  if  any 
vamps  or  casings,  bolt  them 
all  together,  after  being  worked 
off  to  the  plumb;  then  apply  th( 
flexible  strip  from  end  to  end  foi 
the  twist  lines,  both  on  the  con 


Glossary  and  Index. 


xvii 


cave  and  convex  sides,  the  arris 
of  block  pattern  at  the  joints, 
and  minor  axis  will  he  a  guide 
for  the  flexible  strip. 

Valley- rafter...  The  rafter  at 
the  internal  angle  of  a  roof,  as 
opposed  to  the  hip,  which  forms 
an  external  angle;  to  obtain  the 
length  215;  find  the  length  and 
cuts  214;  find  the  cuts  of  Valley 
and  jack  rafters  21.!). 

Vault..  .A  passage  or  room  cover- 
ed with  an  arched  ceiling  of  brick 
or  stone. 

Veneer... Method  of  veneering  a 
cylinder;  preparing  the  Veneer 
154, 1.55, 156;  to  prepare  for  winders 
72;  its  thickness  125. 

Vertix...The  point  from  which 
two  or  more  lines  radiate. 

Vertical-plane..  .One  that  is  per- 
pendicular to  the  horizon. 

VoInte...A  spiral  scroll  in  the 
Ionic,  and  Composite  Capitals. 

Wall... A  structure  enclosing  a 
building  and  supporting  its  parts. 

'Wall-string... How  to  line  off  for 
flyers,  iiO;  for  winders,  94. 

Walnut.  ...  For  hand-rails  and 
finish,  210. 

Well..  .The  vertical  space  in  which 
the  stair-case  is  built;  trimming 
the  well,  99, 100, 116, 117, 118. 


Well-bole... In  a  stair-case,  the 
vertical  clear  space  between  the 
line  of  nosings,  or  the  greatest 
projection  of  any  mouldings 
around  the  cylinder. 

Winders... The  steps  in  a  stair- 
case that  are  wide  at  one  end, 
and  narrow  at  the  other,  used  to 
turn  a  corner  instead  of  a  level 
pace;  patterns  as  a  handy  means 
to  mark  out,  94, 185. 

Window... An  opening  in  a  wall 
to  admit  light,  and  ventilate  the 
room. 

Wire.. .For  sewing  a  belt,  245. 

W^reathed-Rail.  . .  The  twisted 
part  of  a  hand-rail,  as  required 
around  the  cylinder  in  a  con- 
tinued hand-rail  stair-case;  a 
piece  of  work  having  two  curves, 
or  double  curvature  is  termed 
wreathed.  To  find  the  twist  line, 
11-3;  gluing  up  or  building  up 
crooks  for  the  wreath  part.  210; 
best  worked  from  thick  stulT,  210; 

Wreath-piece.. .  Part  of  a  wreath. 

Wreatta-strine'*..The  cylinder  in 
a  stair-case  having  a  double 
curvature  as  when  cut  and 
moulded  to  suit  the  inclination 
of  stairs. 

Yard. . .  A  measure  of  three  feet. 

Zac. .  A  tool  for  cutting  slate. 


KN 


Plate  1. 

I' 


l.^ 


12 


A 


18 


18.0 


h         G 


E 

E 
F 

15    3 

N 

16J?"        6 

L__JO 


Qeometry 


Plate  1 
6 


V 


9 


13 


A 

>B 

/ 

/; 

18 

/ 

/"S 

im"     / 

12 


r 


Plate  2. 


BZQ 


/ 


\ 

\   \ 
/  \  \ 
/     \  \ 
I        \. 


V' 


A-- "     B 


Geometry 


Plate  3. 


fi^ 


A  »         10       Q        **        '        B 


Problems 


( 

4 

\ 

1     ^-  -  '    ' 

.1 [ 


t=0=3 


Plate  3. 


9 


! 


5  c 


>" 


«  II         10       « 


^v 


e  1  2  3  «  '  e 


W«5432»8 


Plate  4. 


!: 

\ 

'o;: 

\ 

^'L 

n  ^'\- 

9 

\ 

r^ 

■\.\-- 

,-^  ~.  --'" 

>  /^\^, 

-i 

\-.- 

V 

1    ^ 

Plate  5. 


/  2 


Plate  5. 


V^ 


Ellipsis 


'  ,,/-- 

f          ■     -    K         1 

\.^ 

'       ^-^^ 

Plate  6. 


B1234    567 


Plate  6. 


Plate  7, 


Plate  7. 


15' Radial  Line 


/^ 


Plate  8. 


Plate  9 


Plate  9 


I 


I 


^'iTioiii"     "'BadiarLine'""o 


Plate  10. 


v. 


Plate  10. 


Plate  11. 


)        Tangent 


^M     \  :4 

i  -^  ^  1  OB 


'^ 


pi^"**is;^' 


Plate  11. 


r^ 


Plate  12. 


Plate  12. 


V 


la 
■3 

// 

y  ^ 
/  / 

/ 

/ 

/ 

•a 

H 

f/ 

I 

/       / 

2 

] 

EJevalioQ 

A 

f/     ~~-jh 

C 

e 

Plate  13. 


Bnt 


e.e 


ce    Mou 


B             Tangent           ^--^^^^t 

m 

1 

''49^ 


f-j^~^4:  Face    Mould 


Plate  13. 


'            TnQgeat                _^          - 

-c/ 

r 

i--^ 

Sj              i-    ««»-C        JII.VIU1U      . 

1^4  Face   Mould 


I 


Plate  14. 


Plate  14. 


E 

H 

D 

!•>             / 

\           / 

<           / 

_N 

11 

F 

'/        >^ 

a 

bo 

A 

^/. 

/-Elevation 

B 

X 

M       )     L 

; 

^,-^,       , 

8 

Plate  15. 


Scale  3^^  I' 


rr  ilO 

Plan 


:\r--    16' 


J 


r    Plan     ; 


Plate  15. 


Plate  16. 


Plate  17. 


Scale  3^=r 


Plan  «    6    > 


14 


Plate  18. 


Plate  18. 


Plate  19. 


Scale  1-4=^1 


Plate  19. 


V 


/  6 


■      Plan             r 

-4  64-9 1 

1 

r   .4 

10           0'  ■ 

9 

16 

8 

16 

S 

6             : 
4         ^' : 

3 

L 

IB 

J 

1    la   p   |4   Is    la   r? 


LL3  -■ 

10   11      12    13     14     16 


Plate  20. 


3 


--if  - 

- 

-?"• 

^M. 

\ 

DC 


9 


-  ^ff(i}mj;,"fiuu""""'^ 


^ 


Plate  20. 


X 

Scale  3^=t'           ^^^-^ 

--"■"''^ 

~:rr==— — T^-       r,"         '.i- 

^^^- 

Plate  21. 


1^ 


Plate  21. 


Plate  22. 


^ 


Plate  22. 


Plate  23 


Plate  23. 


■ftt 


(»A 

10 

: 

:-::::^^ 

^   \ 

IB 

Plate  24. 


Plate  25. 


Scale  1-4—1 


7 -a* 

I      h 

>-4 
8.4" 


D 


•1 


^e1^ 


15 


14' 


18' 


12 « 


9" 

8  i 


7  1 


'8. a 
P 


^1 


i'B      B 


;;  a 


A.' 


:;-4U'; 


:aa 


13 


13 


.  C*.  .   .    .  .1.1- 


B~nsjB^ 


Hi' 


4'.  I  " 


*)K-     -^.z 


Plan 


Plate  25. 


Scale  i:«=l 


I 


Jof 


--'A 


Plan; 


€ 


r 


Plate  26. 


Plate  27. 


Plate  27. 


Plate  28. 


jutv^^» 


^^         Scale  a^=i'' 


Plate  29. 


Scale  3-4=t' 


70h"        ,      6- 'A 


^2  Floods  Llne^4:,  g 

glevatjoD 

15 


Plate  30. 


Scale  3-4=- 1 ' 


Plate  30. 


^ 


::^  s. 

- 

S'H^  .   "fe^ 

r\^ 

^    ^-^^ 

4 

»  x\ 

F 

«.\ 

|. 

17  J 

Eleratlon  / 

. 

//. 

% 

'^ 

<J^-"'l 

B 

Plate  31. 


/^ 


Plate  32. 


V 


Plate  32. 


Plate  38. 


w 


Plate  33. 


Scale  34=1' 


Plate  84. 


V. 


Plate  34. 


3££ag 


r^ 


Plate  35. 


Scale  34=1' 


Plate  35. 


n 


Plate  36. 


ITo.1 


3 


Scale  3^=1' 


Plate  36. 


Scale  8^=1' 


r\ 


Plate  37. 


,j^      lO    ^'^-~^\        Scale  3-''4=l^ 


Plate  37. 


Plate  38. 


Plate  38. 


J p:„  ,xj^-g^^-r-r-: 


v7 


Scale  34=1 


'\l 

17 

IS 

1 

i 

■■tHrik'V 

Io«l«  M^ 


Plate  39. 


Plate  39. 


Plate  40. 


"^  7 

— — 

U^-^ 

^-^^ 

K/ 

<• 

^  ^-? 

*»    , 

.S    <r. 

o 

x;^v 

n 

":^-. 

8 

to'    ^rv 

0 

-> 

7 

■*         ^v 

r>. 

^'     'r3K*  5r    -^     8H 


4-.-.l0"---4 

6 


1 

Pit 


Plate  40, 


Plate  41. 


s.y. 


Plate  42. 


Bcale  1-4=1 


Plate  42. 


1.'^ 


Bc«la  1-4=1 


r*— 


r 


Plate  43. 


Face  Mould 

Scale  3^'4=1' 


Plate  43. 


Plate  44. 


m 


Scale  a^=l' 


10^ 


9\ 


10-3  O  N 


^i^ 


^K 


"^  15« 


No-^ 
/ 


-"^v. 


No-1 


.0-- 


Pian 


-^•^      1        W  c/ 


10-5 


.■-(^         I 


t     m  u 


€^ 

\ 

1 

,_^ 

i^ 

M  ^- 

■ 

o 


V 


Plate  44. 


r-;Jv;:;/-\----- 

jpian 

l^^X.   ,.;j\- l.s 

^   ^ 

13" 

14  ' 

!&■' 

Plate  46. 


V 


Plate  45. 


Plate  46. 


QQsas 


r^ 


Plate  47. 


9'- 6' 


Plate  47. 


C 


Plate  48. 


Plate  48. 


TAB 


in  feet. 


Length  of 
for  1" 
mon  raft 
mals  of 


For  the 
In  coll 
foo 
And  m 


Cutoff 
in  the 


euqals 
And  th 

Equals 
Multipl 


Equals 
Multipl 

Equals 


TABLE  OF  LENGTHS  AND  CUTS  FOB  COMMON  AND  HIP  RAFTERS  FOR  A  HIP  SQUARE  ON  PLAN;  ALSO,  CUT 

OF  JACK  RAFTERS  AGAINST  HIP. 


THE   LENGTH    OF    RAFTERS,    FOB   A   FOOT   RUN,  IS    GIVEN   IN   FEET  . 


DECIMALS    OF   A  FOOT, 


P.TCH..                  1          Vl           1           A 

i 

J       1       *      1       5 

i       1       1       1       J       i       i       1       1       1       1 

GOTHICt 

a  1  a 
g   1  1 

w  1  g 

a  1  sa 
0    1   f 

§     $ 

»  1  a 
§    1  S 

a  1  » 

§  1  s 

c     1   - 

c     1    - 

«    1    » 

»    1    » 

§     1    f 

a  1  w 

a  1  » 
i   1  1 

a    1   » 
£    1   » 

Out  of  common  rafter, 

12»  X  2" 

12"  X  2.4" 

12"X2.066" 

12"  X  3" 

12"  X  3.428" 

12"  X  4" 

12"  X  4.8" 

12"  X  «" 

12"  X  8" 

12"  X  12" 

12"  X  10" 

12"  X  18" 

12"  X  20.7846'' 

Out  of  hip  rafter. 

17"  X  2" 

17"  X  2.4" 

I7"X2.86a" 

17"  X  3" 

17"  X  3.428" 

17"  X  4" 

17"  X  4.8" 

17"  X  6" 

17"  X  8" 

V'  X  12" 

17"X16" 

17"X18" 

17"  X  20.7846" 

Out  of   jack    rafter  t 
a),'ainst  the  hip.        f 

12"  X  12A" 

]2"X12/8" 

12"X12-A" 

12"  X  12li" 

12"X12H" 

12"X12H" 

12"  X  i2ir 

12"  X  13H" 

12"X14JI" 

12"  X  loH" 

12"X20" 

12"X2li!" 

12"X24" 

Length    of    common] 
ratter,  for  12''  run,  } 
in  feet.                       ) 

1.138' 

1.0198' 

1.0344' 

1.0308' 

1.010' 

1.0541' 

1.0770' 

1.1181' 

1.2019' 

1.4142' 

1.6667' 

1.8028' 

1.9999' 

Length  of  hip  rafter  1 
tor  12"  run  of  com-  ■ 
nion  ratter,  in  feet. 

1.42M' 

1.4307' 

1.4340' 

1.4380' 

1.4452' 

1.4654' 

1.4721' 

1.5023' 

15«57' 

1.7341' 

1.9454' 

2.0832' 

2.8376' 

Length   of   common 
rafter  for  1"  run.  in  • 
decimals  of  a  foot. 

o.osiy 

O.OS49!f 

0.08.54' 

0.0859' 

O.OSOff 

0.08784' 

0.0898' 

0.09317' 

O.lOOlff 

0.117a.¥ 

0.1389' 

0.1502' 

0.1066' 

Length  of  hip  ratterl 
fof  1"  run  of  com-  V 
mon  rafter,  in  deci-  1 
mals  of  a  foot.         J 

O.llSlf 

0.U92' 

O.ll'.B' 

0.1197' 

0.1201' 

0.1313' 

0.1227' 

0.12.-12' 

0.1305' 

0.i415' 

0.II121' 

o.nw 

0.1805' 

EXAMFIiE. — Required  the  cuts  and  Length  of  a  rafter  K  pitch  h(ViAng  a  run  of  14'  7";  also  the  cuts  and  length  of  htpfor  the  same. 
For  1 


I  line  for  common  rafter,  take  for  o 

foot  in  length  the  constant 

And  multiply  the  siime  by  the  length  of  rafter  in  feet,  [14'] 


And  the  decimal  .2906,  which  multiply  by  12' 


E(iuals  for  the  length  of  rafter  S 


r  2<y  3SI". 1.5901 


Fob  the  Length  op  Hip  Rafter. 

Take  the  constant  2.0632'  In  same  column 

And  multiply  by  the  length  of  Common  rafter,  in  feet,  [Hl-- 


And  add  the  odd  inches:  for  this  take  the  constant  0.1719  for  hi 
,  and  multiply  by  the  number  of  odd  im- 


['o.in9'X 7=1.2033']  equals  1.20^"fof  the  odd  Inches- 
Gives  SCand  the  decimal  .0981' 

This  multiply  by  12" 

Equals  one  [1"]  inch  and  the  decimal  .0572" 

Which  multiply  by  IB, 


Equals  i^  nearly,  therefore  we  have  for  the  length  of  rafter  30"  liV'- 


For  the  cut  of  common  rafter.— In  the  same  column,  take  12"  on  the  blade  and  18" 
tlie  tongue.    The  blade  gives  the  foot  cut  and  tongue  the  plumb  cut. 

the  blade  and  18"  on  the 
1 

For  tlie  ciU  of  jacks.— Ta.\ie  12"  on  the  tongue  and  2ll§  on  the  blade.  The  blade 
gives  the  cut. 

When  cutting  hip  or  .lack  rafters,  take  the  lengths  and  apply  the  bevel  on  top 
and  at  the  center  of  timber,  dividing  the  miter  equally  each  way. 

For  the  cut  of  hip  rafter  0(/aiiw(  the  rtdne  p(<Ue— Take  Its  length,  BR  Fig.  2,  on  the 
blade  and  the  side,  which  is  equal  to  the  run  DE  on  the  tongue;  the  blade  gives  the 
ent.  Remember  the  run  only  applies  when  the  hip  is  square  on  the  plan,  as  at 
Fig.  1.  When  rectanuular  on  plan,  ox  at  F(g.  a.  Take  the  length  CB  on  the  blade  and 
the  side  DR  [as  for  a  jack  rafter]  on  the  tongue.    The  blade  gives  the  cut,  provided 


iiade  before  the  backing  is  done. 


•Any  pitch  defined  s 


3  that  the  rise  of  rafter  equals  A  ( 
_    _     „'.    As  for  a  comb  roof,  having  a  spn 
uld  equal  18  feet,  which  would  be  a  rise  for  a  shed 


.  pitch,  the  ris 
roof,  or  lean-to,  equal  to  30  feet. 

+The  rafter  is  equal  In  length  to  the  span,  forming  an  equilateral  triangle  for 
a  gothlc  pitch. 

1  For  struts  and  braces,  havingthe  same  rise  and  run.  17"  is  allowed  for^each 
foot  run  for  the  length  of  brace.    This  is  a  little  full;  the  correct  i 
lii.!»705".  the  difference  being  a  scant  ^  of  an  inch. 


being 


PLATE  49-APPENDIX  No.  I, 


APPLICATION  OF  THE  STEEL  SQUARE  IN  ROOF  FRAMING. 


Pig.  1.  Shmvs  plan  of  a  square  hip.  Fig.  2.  Shows  the 
elevation. 

DCEF  shows  plan  of  hip  and  jack  rafters ;  DE  is  the  seat 
of  tlie  hip,  having  an  augle  of  45  degrees  with  the  walls  ;  DC  is 
the  run  of  a  common  rafter,  and  DB  the  rise ;  BC  is  the  length 
of  a  common  rafter.  Make  DR  equal  DE,  join  BR  for  the 
length  of  hip  rafter  :  from  D  and  at  right  angles  to  BR  draw  DS; 
perpendicular  to  JSCdraw  BH ;  Z  shows  the  purlin. 

For  the  cuts  and  length  of  common  rafter  BC. — Take  the 
run  DC  on  the  blade  and  the  rise  DB  on  the  tongue  all  to  a  scale. 
The  blade  gives  the  foot  cut  and  the  tongue  the  plumb  cut,  as 
shown  at  6  and  4  ;  the  hypothenuse  BC  gives  the  length. 

For  the  cuts  and  length  of  hip  rafter  BR.— Take  the  run 
DE  on  the  blade  and  the  rise  DB  on  the  tongue  to  a  scale.  The 
blade  gives  the  foot  cut  and  the  tongue  the  plumb  cut,  as  shown 
at  7  and  5  ;  the  hypothenuse  BR  gives  the  length. 

For  the  cut  of  jack  rafter  2  3  against  the  hip. — Take  BC  on 
the  blade  and  the  level  side  CE  on  the  tongue.  The  blade  gives 
the  cut,  also  the  cut  of  hip  against  the  ridge  plate  if  applied  on 
the  plane  of  backing,  and  from  the  side  of  hip  in  which  the  jacks 
are  parallel  with  the  ridge,  [if  on  the  opposite  side  of  hip,  then 
the  tongue  gives  the  cut].  It  also  gives  the  miter  for  the  gable 
mouldings  and  planceer  in  a  raking  cornice.  The  tongue  gives 
the  miter  cut  of  purlin  against  the  hip,  also  sheathing,  gutter  stop 
and  level  planceer  when  canted  to  the  pitch  of  rafters ;  the  foot 
and  plumb  cuts  are  the  same  as  for  the  common  rafter  shown  at  6 
and  4.  The  length  of  jack  rafters  may  be  established  by  squaring 
up  from  plan  to  common  rafter  as  shown  at  abc,  and  as  described 
at  Figs.  1  and  2,  riate  49. 


2 


Appendix  No.  1. 


Foi-  the  cut  on  edge  of  sheathbig. — Take  BH  on  the  blade 
and  DH  on  the  tongue.  The  tongue  gives  the  cut,  also  the  side 
cut  of  purlin  against  the  hip,  gutter  stop,  and  level  planceer,  when 
canted  to  the  pitch  of  rafters. 

For  the  hacking  of  hip  rafter. — Take  DE  on  the  blade  and 
DS  on  the  tongue.  The  tongue  gives  the  bevel  ;  the  angle  for 
saddle  on  hip  may  be  laid  off  from  this  bevel  if  required. 

To  find  the  cut  on  the  lower  end  of  a  hip  or  valley  rafter  to 
line  ivith  the  common  rafter,  wlien  they  are  cut  square  instead  of 
plumb,  for  the  corona  in  a  raking  cornice. — From  D,  Fig.  2,  and 
perpendicular  to  CB  draw  Dn,  draw  no  parallel  to  DC,  join 
DO.  The  angle  at  O  gives  the  bevel.  Take  12^''  on  the  blade,  and 
adjust  the  tongue  to  DO  from  the  line  BO,  the  tongue  gives  the 
cut. 

The  above  cuts  for  jack  rafters,  purlins  and  hip  backing',  are  for  hips 
when  square  on  plan.  When  rectangular  on  plan,  follow  Fig-s.  3, 4  and  5. 


Pig.  3.  Shows  plan  of  a  hip  aceommodctting  tiuo  pitches i 
the  seat  GD  of  hip  being  the  diagonal  of  a  rectili7ie(il  parallelo- 
gram ADJG  on  plan.  Figs.  4  and  5  sfww  tlie  elevation  of 
common  rafters. 

AD  is  the  run  and  DB  the  rise  for  the  rafter  AB;  AG  \s 
the  run  and  AK  the  rise  for  the  rafter  GK;  [BE  has  the  same 
inclination  as  ASj.  Perpendicular  to  BE  draw  BH;  at  right 
angles  to  AD  draw  HL.  Make  DC  equal  DG,  join  BC  for 
length  and  inclination  of  hip  rafter.  From  D  and  at  right  angles 
to  SCdraw  DS;  from  D  and  square  to  DG  draw  a  line  to  inter- 
sect GA  prolonged  at  Q,  also  intersect  GJ  produced  at  jR;  at 
right  angles  to  KG  draw  KP,  Make  23 Jlf  equal  AP;  from  M 
draw  a  line  parallel  with  Gr J"  to  intersect  DG  prolonged  at  N. 


Appendix  No.   I.  3 

For  the  cuts  and  length  of  covimon  rafter  ABfor  the  side 
AGD. — Take  the  run  AD  on  the  blade  and  the  rise  DB  ou  the 
tongue  to  a  scale.  The  blade  gives  the  foot  cut  and  the  tongue 
the  plumb  cut.  as  shown  at  4  and  5  ;  the  hypothenuse  AB  gives 
the  length. 

For  the  cuts  andlength  of  hip  rafter  CB.— Take  the  run  GD 
on  the  blade  and  the  rise  DB  on  the  tongue  to  a  scale.  The  blade 
gives  the  foot  cut  and  the  tongue  the  plumb  cut,  as  shown  at  6 
and  9  ;  the  hypothenuse  CB  gives  the  length. 

For  the  cut  of  jack  rafters  against  the  hip. — Take  AB  on  the 
blade  and  the  level  side  AG  on  the  tongue.  The  blade  gives  the 
cut,  also  the  cut  of  hip  against  the  ridge  plate,  if  applied  on  the 
plane  of  backing  and  from  the  side  in  which  the  jacks  are  parallel 
to  the  ridge  plate — [if  applied  from  the  opposite  side  then  the 
tongue  gives  the  cut].  The  blade  also  gives  the  miter  cut  for  the 
gable  mouldings  and  planceer  in  a  raking  cornice  ;  the  tongue 
gives  the  miter  cut  for  the  purlin  against  the  hip.  sheathing,  gutter 
stop  and  level  planceer  that  is  canted  to  the  pitch  of  rafters.  The 
foot  and  plumb  cuts  are  shown  at  4  and  5  for  the  jacks,  and  their 
lengths  are  found  in  the  same  manner  as  described  for  Figs.  1  and  2. 

To  find  the  side  cut  for  purlin. — Take  S^Ton  the  blade  and 
and  HL  on  the  tongue.  The  tongue  gives  the  cut,  also  the  cut 
for  sheathing  on  its  edge,  also  the  gutter  stop,  and  level  planceer 
when  canted  to  the  pitch  of  rafters. 

To  find  the  heveifor  backing  the  hip. — Take  DQ  on  the  blade 
and  DS  on  the  tongue.  The  tongue  gives  the  bevel  for  one  side 
of  hip. 

For  ciits  and  length  of  ioninion  rafter  GK,  on  the  opposite 
side  GDJ. — Take  the  run  GA  on  the  blade  and  the  rise  AK  ou 
the  tongue  to  a  scale.  The  blade  gives  the  foot  cut,  the  tongue  the 
plumb  cut.  as  shown  at  8  and  7  ;  the  hypothenuse  GK  gives  the 
length ;  CB  shows  the  length  and  cuts  of  hip. 

For  the  cut  of  jack  rafter  To  a{iai)istthehip. — Take  GKon 
the  blade  and  GJ  on  the  tongue.  The  )>lade  gives  the  cut,  also 
cut  of  hip  rafter  against  the  ridge  plate,  provided  it  is  applied 
on  the  plane  of  backing  and  from  the  side  in  which  the  jacks  run 
parallel  to  the  ridge  plate — [if  applied  from  the  opposite  side 
then  the  tongue  gives  the  cutj.  The  blade  also  gives  the  miter 
cut  for  the  gable  mouldings  and  planceer  in  a  raking  cornice; 
the  tongue  gives  the  miter  cut  for  the  purlin  against  the  hip. 
sheathing,  gutter  stop,  and  level  planceer  to  suit  the  pitch  of 
rafters  ;  4  and  5  show  the  foot  and  plum  cuts  :  their  several  lengths 
are  described  at  Figs.  1  2,  and  5. 

For  the  side  cut  of  p^irlin. — Take  KP  on  the  blade  and  MN 
on  the  tongue.  The  tongue  gives  the  cut,  also  the  cut  for  edge  of 
sheathing,  gutter  stop,  and  level  planceer  to  suit  the  pitch  of 
rafters. 

Bevel  for  the  backing  of  hip  rafter. — Take  DR  on  the  blade 
and  DS  on  the  tongue.  The  tongue  gives  the  bevel  for  the  one 
side,  and  together  with  the  bevel  for  the  opposite  side  will  give 
the  angle  for  the  saddle  on  hip  if  required. 

The  points  a^b,  c,  d,  e,  Fig.  5,  show  the  lengths  of  jack 
rafters  for  the  side  GDJ;  the  half  thickness  of  hip  must  be  de- 
ducted. Remember  in  deducting  the  half  thickness  of  hip,  or 
ridge  plate  when  required,  it  must  be  measured  square  to  the  plane 
of  the  cut  and  not  square  to  the  plumb  cut.  The  lengths  Ga, 
Gb,  &c  ,  as  here  drawn,  are  to  the  center  of  hip,  and  the  hips  to 
the  center  of  ridge  plate. 


Appendix  No.  1. 


?h 

1 ^ . 

1 

^ 

\ 

^ 

R 

is 

1          i 
1          1 
1          1 

1 

'\ 

>1 

y       A 

r<^^ 

-1 

_   Run  1 

H 

\ 

\   ^T"      Rise 

1 

0 

8 

7 

/ 

/ 

\ 
\ 

\ 

- 

1/ 

c 

e 

/ 

^ 

\\        ^ 

/ 

^ 

5\  \      j 

/ 

V 

/a 

/ 

b 

\ 

s. 

/ 

/ 

c 

D 

y 

/ 

W 

/ 

B 


P 


Fig.  1. — {Scale,  one-eufhth  inch  equals  one  foot).  Shoivs 
one  side  of  a  roof  haiying  a  %  'pitch  and  a  square  hip  and  valley. 
How  to  find  the  length  of  valley  and  cripples  hetioeen  the  valley 
and  hip. 

A,  S,  C,  D,  E,  F,  shows  the  plan  of  roof ;  EB  shows  hip, 
DH  shows  seat  of  valley  ;  ab.  cd,  e/ shows  the  seat  of  cripples  ; 
CA  is  a  gable  and  AJ3"the  ridge. 

Draw  JBJ'for  the  rise  ;  make  .5.2"  equal  EF;  join  JJTfor  the 
length  of  common  rafter.  From  H,  and  perpendicular  to  AB, 
draw  a  line  to  intersect  the  common  rafter  at  M,  then  MH  is  the 
rise  of  valley  rafter.  Make  HN  equal  HD ;  join  MN  for  the 
length  and  cuts  of  valley  rafter. 

For  the  length  of  cripple  ab. — From  the  points  a  and  b  erect 
perpendiculars  to  inteisect  the  common  rafter  JK  at  2  and  3  ;  the 
valley  and  hip  being  both  parallel,  then  the  distance  2  3  is  the 
length  for  all  the  cripples  between  the  hip  and  valley  rafters. 

For  the  length  of  cripples  between  the  ridge  and  valley 
ra/ter.— Make  AP  equal  the  rise  HM;  join  PC  for  the  length 
and  cuts  of  the  gable  rafter.  From  the  points  a,  c,  e,  erect 
perpendiculars  to  CA,  cutting  PC  at  4,  .5  and  6 ;  then  P4,  Po 
and  Pa  show  the  length  of  cripples  e7,  C8  and  a9  on  plan. 

Fig.  2.    {Scale  three-eighths  inch  equals  one  foot).    Sliows 
the  template  for  marking  the  heel  and  side  cuts  of  jack  rafters. 
A  shows  the  side  and  B  the  top. 

The  cuts  for  the  cripples  at  the  valley  rafters  are  the  same  as 
for  a  hip  rafter,  only  the  plumb  cut  is  the  reverse  way,  the  long 
point  being  on  the  under  side,  ^ 


Plate  49. 


Plate  49. 


I 


Plate  50. 


Plate  51, 


flPPEflDlX    Ho.    2. 


PLATE  52. 

Plate  52.  [Scale  >s=i  J  Square  Hip  and  Octag"on 
Roof  Framing'. 

Fig'.  8.  Shows  a  practical  and  simple  metJiod  lioio  to  devclope 
the  length  and  cuts  of  the  common  hip  and  jack  rafters  on  the 
pitching  plane,  for  a  square  hit)  and  for  any  pitch. 

Let  ABCD  be  the  plan  for  two  square  hips,  and  AF,  FB  he 
the  seal  of  hips;  draw  the  seat  of  jack  rafters  to  intersect  the  seat  line 
of  hip,  as  FF,  et,  di'f  <Cr.  Make  Etf  equal  Fli  join  FrT  for  the 
length  and  cuts  of  the  hip  rafter.  It  will  be  observed  now  for  a  half 
pitch  roof,  we  have  the  length  of  hip  tTF:ind  the  common  rafter  AF 
and  the  length  of  the  jack  rafters;  ^It  equals  the  length  of  jack  to 
stand  over  the  seat  et:  Ar  to  stand  over  dr,  <{'<'.  . 

Bevels.  The  bevel  at  ,S  gives  the  down  and  foot  cuts  for  the  corin- 
nion  and  jacks  rafters:  the  bevels  at  ?>  and  JO  give  the  down  and 
foot  cuts  for  the  hip  Fr/;  for  the  cut  of  jacks  against  the  hip,  jirolong 
dr  to  equal  its  length  Ar,  as  (If/,  join  Aff  for  the  bevel  at  ry. 
For  the  cut  of  hip  against  the  ridge  plate  at  _//;  take  any  point  on  the 
seat  FT*  of  hip,  say  at  the  intersection  of  the  jack  from  I  at  II, 
draw  tirj  at  right  angles  to  FH;  from  ii  and  parallel  to  the  base 
line  Ali,  draw  a  line  to  intersect  the  hip  as  i(S,'  make  i((i  equal 
'f'i,  join  Lfi  for  the  bevel  as  shown. 

This  completes  the  drawing:  for  a  pair  of  rafters,  two  hips  and  the  length 
of  ()  jack  rafters  and  the  cuts  for  the  same  for  a  |^  piteh  roof;  the  bevel  as 
shown  for  the  cut  of  hip  against  the  ridge  plate  is  applied  before  backing. 

For  a  }^  pitch  the  principle  is  the  same;  let  F{r  be  j^  the  span 
AB,  join  ^Ifr  and  (xBy  the  intersection  with  the  seat  of  jacks  gives 
the  length  of  jack  on  the  common  rafter  Afr  as  at  z  and  s/  Atf  is 
the  length  of  the  jack  to  stand  over  its  seat  et,  and  so  of  all  the  rest 
respectively.  For  the  length  and  cuts  of  hip,  join  (rJy  for  the  cut  of 
hip  against  the  ridge  plate,  from  /.■  draw  h-2,  make  W.T  equal  fJ2. 
join  .)L  for  the  bevel  at  ,5.'  for  the  cut  of  jack  against  the  hip  prolong 
the  seat  of  jack  ef  to  equal  its  increased  length  As  as  eh,  join  Ah 
for  the  bevel  as  shown. 

I^or  a  J/t,  pitch  this  system  is  the  same.  Let  FII  equal  %  the 
span  AB,  join  AJl  and  Blifor  a  pair  of  common  rafters  and  their 
cuts;  join  HJ  iox  the  length  and  cuts  of  hip  rafter;  for  the  length  of 
the  jacks  prolong  their  seats  to  insert  the  common  rafter  at  x  and  y: 
then  Al/  is  the  length  of  jack  to  stand  over  its  seat  et,  and  so  of 
all  the  rest;  for  the  cut  of  jack  ?gainst  the  hip,  prolong  the  seat  Bit 
to  equal  its  increased  length  Ap.  as  bf,  join  Af  for  the  bevel 
required  at/'.  For  the  miter  of  hip  against  the  ridge  plate,  prolong 
/«  to  ir,  draw  *r -i^  parallel  to  ^IB,-  make  /^  7  equal  J-t:,  join  7 
Li  for  the  bevel  as  shown. 

This  is  the  most  simple  method  to  line  off  a  sipmre  hip.  less  linps  ard 
room  is  required  by  this  system:  if  the  hip  be  backed  less  lines  may  be 
used,  the  bevels  sb.own  at/,  r/and  h,  for  the  jacks  will  also  give  the  miter 
cut  for  their  respective  hips  ngaiubt  the  ridge-plate  if  applied  on  the  plane 
of  backing.  Pl.^te  49  shows  the  most  practical  method  to  obtain  the 
difl'erent  bevels,  also  the  backing. 

The  young  man  should  first  study  how  to  draw  the  lines  on  the  board  for 
a  hip  and  valley  ronf.  then  from  the  drawing  thus  made  to  a  %"  scale, 
proceed  to  frame  the  mof.  For  a  square  liip  it  is  very  easv  to  a])i)lv  the 
sfpiare  for  all  the  princijial  cuts,  but  for  a  hip  or  valley  that"  accommodates 
two  pitches  it  is  more  difticult.  a  drawing  then  is  necessary,  and  if  the 
student  (irst  learns  to  draw  otf  the  roof,  he  afterwards  will  be  better  qnali- 
Med  to  tind  his  way  out  when  framing  one  more  complicated,  even  v.\X\i  the 
steel  square. 

Fig'  9,  [Scale  y%  =i  ]  Shams  the  end  of  a  building  finished 
ivith  acta  zona  I  corners. 

The  octagon  is  carried  up  to  the  comb  of  main  roof  instead  of  a 
gable;  one  side  of  the  octagon  to  admit  windows  is   shown  increased 


in  widlh,  the  cornice  is  to  project  the  same  at  the  eaves  and  to  be  rak- 
ing; unless  the  workman  has  had  some  experience  in  the  framing  of 
such  a  roof  he  may  be  taken  unawares. 

Let  AB,  BC,  CD,  DE  and  EF,  Fig.  9,  indicate  the  outside 
measurements  of  walls  and  dll,  HJ^  JK,  KL  and  iJXlhe 
projection  for  the  ends  of  ratters  to  receive  the  cornice.  Now  from 
the  points  II,  «/,  K  and  L  draw  lines  to  the  centre  O  for  the  seat 
lines  of  hips,  also  space  off  and  draw  the  seat  of  jack  rafters  as  may 
be  desired. 

Let  it  be  observed  that  the  seat  of  hips  does  not  intersect  the  angle  of 
walls  at  the  poiitts  BCL  and  E,  but  cuts  to  one  side,  tliis  cannot  be  avoided 
in  a  roef  with  two  jiitches  and  a  raking  fornice,  for  the  look-outs  (or  a  cor- 
nice having  the  same  projection  all  around  and  of  different  pitches,  the 
points  of  hips  and  other  ratters  must  be  on  the  same  level,  therefore  we  must 
draw  their  seats  from  the  utmost  projection.  If  the  cornice  was  a  level  one 
then  the  seat  of  hips  may  be  drawn  from  the  points  BCD  aud  E. 

Now  ^J^  equals  the  span  of  building  and  OG,  OJM  and  Of, 
show  the  seat  of  common  railers  and  they  are  equal  from  the  centre 
O;  but  the  seals  OA",  Otl  are  longer,  therefore  we  have  two  pitches; 
Ihe  planes  03IL,  OQH and  OJK  have  the  same  pitch;  but  the 
planes  OHtJ  and  OKL  have  a  flatter  pitch;  their  length,  pitch  and 
location  of  the  wall  plates  must  be  determined  by  drawing  them  in 
elevation. 

Fig.  10.  S/i07i'S  in  elevation  the  pitch  and  length  of  the  different 
rafters,  also  the  location  of  the  tvall plates,  all  on  the  pitching  plane. 

Draw  the  base  line  XX ;  from  h  erect  the  perpendicular  ho 
equal  to  the  rise  of  roof;  make  hu  equal  OA.  Fig.  9;  draw  OCI 
prolonged  to  intersect  the  horizontal  projection  of  rafter  at  C;  from  C 
and  parallel  to  J^TJE^draw  ctll  indefinate;  now  the  points  of  all  the 
rafters  must  terminate  at  this  line  cm  as  shown.  At  ff  is  shown 
the  wall  plate;  next  set  off  the  width  of  look-out  required  for  the  cor- 
nice and  draw  the  back  of  rafter  intersecting  ho  at  V,  then  VO  is 
the  heighth  above  the  plate  on  line  with  the  wall  at  ci  for  all  the 
rafters. 

Make  hd  equal  Ot  on  plan  Fig.  9;  draw  0(l  prolonged  to 
intersect  the  line  mc  at  <y/  from  «'  and  parallel  to  0(/  draw  the 
back  of  hip  rafter,  the  common  and  hip  rafter  are  now  the  same 
plumb  heighth  on  the  plates  (I  and  cl,  at  the  wall  line.  Make  In 
equrl  OK  Fig.  9,  join  on;  thus  establishing  the  flatter  pitch  for  the 
planes  OKL  and  OH  J  on  plan  Fig.  9.  Make  Jp  equal  O.S  Fig.  9; 
from  p  erect  the  perpendicular  intersecting  oil,  at  *>  draw  SK,  thus 
establishing  the  position  of  the  wall  plates  for  the  flatter  pitch  relative 
to  the  wall  plates  for  the  steeper  pitch;  observe  the  plate  at  s  drops 
down  below  that  at  <l  about  i^2»  this  will  require  the  plates  BC 
and  I)E  Fig.  9  to  be  framed  1^2  lower  than  those  for  AB,  CI^ 
and  EF,  as  the  difference  in  this  case  is  so  little  another  way  would 
be  to  notch  out  at  s  1)4  '  more  on  all  the  jacks  and  construct  all  the 
plates  to  the  same  level  if  the  look-outs  would  not  be  too  much 
weakened,  this  the  workman  would  be  governed  by  his  judgement. 
Make  Im  equal  the  seat  OL  Fig.  9,  join  oni  intersectirg  ab  pro- 
longed at  ry  from  v  draw  the  back  of  common  rafter  paralell  to  so 
and  also  the  back  of  hip  rafter  parallel  to  Oill,  thus  establishing  their 
proper  heighth  above  the  plates  at  the  wall  line. 

Next,  draw  the  length  of  jacks  from  plan  to  elevation  as  shown 
the  length  of  jacks  ile,  <(h  and  tjh  on  plan  Fig.  9,  are  shown  in  eleva- 
tion as  t'Cr.  CE  and  lit.  The  jack  r?e  on  plan,  scales  [3'  io_j4-|- 
l',  7|<=5',  6  ]  in  elevation  5-6';  the  jack  f(h  on  plan,  scales 
[i' 3' -|-i' 7>^''=3' 10^']  in  elevation  3',  io}i-,  the  rafter  at/' 
on  plan  buts  the  end  of  ridge  plate  and  scales  [6'  3"  plus  i'  7}4" 
equals?',  loj^^  '  ]  in  elevation  7,  10^'  for  the  total  length  to  the 
long  points;  the  length  of  jacks  for  the  ])lanes  OrJK  and  0 1,31  arc 
the  same  as  for  the  plane  OCH.  The  length  of  jack  yh  on  plan 
scales  [2,  7^ ''-|-i,  6^=4,  2]  in  elevation  4',  2  for  its  total 
length;  the  jacks  at  11  and  /«  on  plan  miter  between  two  hips,  and 
scale  [6',  7   -j-i  ,  6^=8,  lyi'']  to  the  long  point   8,    i^   in  tleva- 


tion;  the  common  rafter  GO  miters  to  the  hip  OH  and  scales 
[6  ,  7>^   -|-i'>  7/^    =8  >  2' ]  in  elevation  8    2   .       The  two  hips    OL 

and  O/i" miter  to  the  ridge  plate  and  scale [7,  3  '4" I  »  9/^=9  >  O  /^] 
for  their  length  9,0^';  the  hips  OrT  and  OK  on  plan,  miter 
against  the  ridge  and  adjacent  hips  as  shown  and  scales  [7',  o"-(- 
1',  9^  =8',  9^  ]  for  their  length  in  elevation  8',  gl^z  '.  Observe 
the  lower  end  of  hip  is  cut  to  the  bevel  at  i  and  the  length  is 
measured  square  from  the  point  at  q,-  make  all  measurements  on  the 
back  of  rafters  by  first  lining  oft  for  the  projection  of  cornice  to  the 
line  of  wall,  then  the  exact  length  from  wall  to  the  point  of  rafters; 
use  a  template  shown  at  Fig.  7  to  line  off"  all  look-outs  and  cuts  for 
the  different  rafters. 

Observe  at  t  on  plan  the  seat  of  hip  intersects  the  line  of  wall  to 
one  side  of  the  angle  CV  now  in  mitering  the  planceer  the  centre  of 
hip  will  be  the  centre  of  miier,  this  will  look  bad,  as  the  miter  should 
run  from  angle  e/ to  angle  C/  to  accomplish  this  two  methods  may  be 
adopted,  either  to  cut  the  look-outs  for  the  planes  OCrH.  OJIi.  and 
OJlLi  by  dropping  as  shown  by  the  dotted  lines  at  C  and  q  Fig  lO 
and  thus  make  the  pitch  for  the  planceer  agree  with  the  lesser  pitch 
OSj  or  to  make  the  pitch  of  planceer  for  the  lesser  pitch  OS  agree  with 
the  greater  pitch  0(f  by  reducing  the  look  outs  at  ,S'  as  shown  by 
the  dotted  line,  this  reduction  will  only  be  for  the  three  jacks  on  each 
side  for  the  odd  pitch,  the  hips  and  all  other  ralters  will  remain 
straight;  the  better  way  then  will  be  to  make  the  underside  of  look- 
outs for  the  lesser  pilch  agree  with  those  of  the  greater  pitch  in  this 
case;  this  will  allow  the  raking  planceer  to  miter  from  angle  to  angle. 

Bevels.  The  bevels  at  «  and /'give  the  foot  and  down  cut  for 
all  the  common  and  jack  rafters  for  the  steep  pitch;  the  bevels  shown 
at  Jt  and  *■,  give  the  foot  and  plumb  cuts  for  the  lesser  pitch;  the 
bevels  at  fl  and  o  give  the  foot  and  down  cuts  for  all  the  hips.  J^or 
the  cut  of  hip  at  the  lower  end  to  agree  loith  the  square  ends  of  the 
Jacks.  From  b  and  perpendicular  to  the  back  of  rafter  oc  draw  hb, 
draw  hi  paralell  to  JSlAT,  join  bi  for  the  bevel  shown  at  //  this  bevel 
gives  the  cut  on  side  of  hips  for  the  planes  OGII,  03IL  and  OJK; 
for  the  opposite  side  of  hips  on  the  planes  OH'f  und  OKL  Fig.  9; 
from  JiL  and  perpendicular  to  the  back  of  rafter  SO  draw  ivH;  draw 
wy  parallel  to  JCX,  join  yk  for  the  bevel  required. 

J^or  the  mitre  cut  of  hips  HO  and  LO  against  the  ridge- plate. 
Apply  the  bevel  shown  at  (i  to  the  sole  cut  of  hip  as  shown  for  Plate 
49,  this  bevel  will  also  give  the  cut  on  top  of  the  hip  at  the  lower  end 
for  one  side,  for  the  opposite  side  on  the  lesser  pilch  the  bevel  at  */" 
applied  in  the  same  way  will  give  the  cut. 

For    the    cut    of  jacks    against     the     hips.  On     plan     Fig. 

9  prolong  lib  to  equal  its  increaseed  length  in  elevation  as 
Cic,  join  c  to  the  side  ot  rafter  at  y;  the  bevel  at  c  gives  the  miter 
cut  lor  all  the  jacks  on  the  planes  OGM,  Ot/K  and  OJML,  the  bevel 
in  the  angle  at  //  gives  the  cut  for  the  sheathing  and  edge  cutof  corona, 
also  the  cut  of  the  two  hips  HO  and  LO  against  the  ridge  plale,  also 
for  the  back  of  hips  at  the  lower  end  for  the  above  planes  if  applied 
after  backing. 

The  same  bevels  may  be  found  from  the  sole  cut  of  com- 
mon rafter  by  applying  the  bevel  at  3,  also  the  miter  cut  for  the 
hips  Oltand  OJa-i  their  upper  ends  by  applying  the  bevels  shown  at 
4  and  i)  Fig.  9  For  the  cut  of  jacks  against  the  hips  on  the  planes 
OH'T-And  OKL;  prolong  the  seat  of  jack  (fit  to  equal  lit  in  elevation, 
as  (fl  join  ii'i  the  bevel  at  i  gives  the  cut,  the  bevel  at  V  gives  the  cut 
of  sheathing  also  the  edge  cut  of  corona  and  the  cut  on  the  back  of 
hips  at  the  lower  end  if  applied  after  backing. 

To  find  the  bevel  to  miter  the  plnvceer.  If  the  planceer  was  to  miter  so  as  to 
agree  with  the  hips  as  drawn,  then  tlie  bevels  slifiwn  at  H  and  K  would  give 
the  initer  cut  for  their  respective  pitches,  and  the  bevels  shown  at  z  and  j 
would  give  the  cut  on  the  edge;  also  for  the  edge  cut  of  sheathing. 

But  the  look-outs  being  all  cut  to  agree  with  the  regular  pitch  oa/ 
then  from  E  Fig.  9,  and  perpendicular  to  KL  draw  JEx  prolonged  to 


equal  cct  Fig.  lo,  as  at  7%  join  »'X,  the  bevel  at  L  gives  the  miter  cut 
fur  llie  p'anceer  ;  for  ike  cut  on  the  edge  of  planceer.  At  Jig.  Ji 
draw  the  right  angle  ,Hp)il,  let  sil  be  the  inclination  of  the  look-out 
on  its  under  side,  and  f^i)t  equal  the  pilch  of  the  miter  over  the  seat 
EL  on  plan  Fig.  9;  from  p  and  perpendicular  to  Sll.,  draw  pf 
from  t  and  paralicl  10  j)}n  draw  f}%wjth  P  for  a  centre  and  2iV  for  a 
radius  draw  arc  to  intersect  sn  at/',  join/'p  for  the  bevel  required. 
J^07-  ilie  cut  of  corona  or  outer  fascia  on  the  eaves  Gli,  311^  and 
tJK  Fig-  9  Return  to  Fig,  10,  wiih  h  for  a  centre  and  hi  lor  a 
radius  draw  arc  to  intersect  Vd  at  J.  join  j7>  for  the  bevel  required. 
For  the  bevel  on  the  ea.\esllrf  and/i[L,  Fig.  9;  at  Fig.  lO  take  Ic  for  a 
centre  and  Icj/  for  a  radius  drnw  arc  to  intersect  the  back  of  rafter  vn 
at  z  .'"or  the  bevel  required.  These  two  bevels  also  give  the  edge  cut 
of  sheathing  on  their  respective  planes,  also  in  case  purlines  are  used 
they  give  the  side  cut  against  the  hip  rafters. 

F.igS-  11  and  12.  [Scale  ^■^"==i']  Shows  the  plan  and  eleva- 
tion of  a  spire  on  an  octagon  base  attd  how  to  obtain  the  lengths  and 
cuts  of  timbers. 

Fig  11.  Shows  one  half  the  pian.  Draw  the  rectangle  ^2>^/i. 
for  one  half  the  plan,  biscei  Alt  at  I.;  w:th  (r  lor  a  center  and  the 
diagonal  (rL  for  a  radius,  draw  the  arc  from  L,  to  K;  make  HT'^GC, 
CrJJ,  equal  jf//<J;  jomEF  and  C'jD  for  one  half  the  octagon  base.  Join 
T-iC  LI>,  JLE  and  Lh\  for  the  seat  of  the  hips;  (i,  a,  shows  twisted 
irons  boiled  to  the  girls  and  hips  for  binders  at  the  several  bays. 

Fig.  12.  Shoius  the  length  and  cuts  of  the  hips,  girts  and  struts 
in  elevation  and  development 

Let  ^1  JJiuilicate  a  base  line,  draw  X/lT  perpendicular  to  ^S,  make 
IjD  and  jLi!^  equal  7v/>  and  KE  on  plan  Fig.  1 1 ;  also  make  EA  and 
EB,  equal  EA  and  EH  on  plan  Fig.  1 1.  Make  EC,  equal  EC  on 
plan.  Now  determine  the  height  of  spi^e  as  EI,  join  IB  and  I  A, 
for  the  inclination  of  the  side,  join  JC  for  the  inclination  of  the  hip; 
I///  shows  tl'C  girts. 

To  find  the  development  of  one  side  of  the  spire ;  make  Ltf 
equal  ^il,  join  JI)  and  JE,  pavaliel  to  »//>  and  tlE,  draw  the  face 
of  backing;  make  Lzz,  equal  AtJiJ,  for  the  spacing  of  the  girts.  Now 
draw  the  struts  as  shown,  tins  gives  all  the  miters  or  face  cuts  for 
the  struts  and  girts  for  the  different  bays;  the  beve'  shown  atj>  gives 
all  the  miter  cuts  fn- the  girts;  the  bevels  at  5  and  t#,  give  the  miter 
cuts  f>r  the  struts  in  the  first  bay;  the  bevels  shown  at  jj»  and  d,  gives 
the  miter  cuts  for  ihe  struts  of  the  second  bay;  those  for  the  upper 
bay  are  shown  in  lite  proper  place.  The  bevels  at  it,  t  and  V  give  the 
cu;s  at  the  crossing  o(  the  stmts. 

Now  for  the  side  cut  of  the  girts  and  struts  against  the  hips  ;  drav/ 
the  dotted  lines  sq,  pO  and  mn  at  the  center  of  the  struts  and  to 
intersect  ihe  sides  rJD,  EE,  and  also  the  perpendicular  tJE,  at  the 
points  a,  t  and  r.  Mzke  Ah,  Ac  and  ^1?>  equal  I^u,  Et  and  Er; 
from  It,  e  and  <l,  draw  perpendiculars  to^X  intersecting  ErI  a.\.  O,  e 
and/'.  No7Cj  for  the  side  cut  of  girts  against  the  hip;  from  6,  and 
parallel  to  AB  draw  hh,  join  ah  prolonged;  with  (i  for  a  center  and 
(iIIlov  a  radius  draw  arc  to  intersect  the  inclination  ^-IjTat  *,  join  ai 
for  the  bevel  required.  If  the  girts  are  to  be  gnined  into  the  hips, 
the  bevel  at  h  gives  the  cut  on  the  hip.  For  the  side  cut  of  the 
struts  aga'nst  the  hips.  At  ?t,  and  perpendicular  to  tWiX  draw  ug, 
equal  to  ha  \o\w  ffni,  also  tpi;  the  bevels  at  m  and  n  give  the  side 
cut  for  all  the  struts  of  the  first  bay;  for  the  second  bay,  from  t,  and 
perpendicular  to  po,  draw  fj  equal  to  ce,  join  jp  and  jo  for  the 
bevels  at  p  and  o  required  for  the  side  cuts  of  all  the  struts  for  the 
se;ond  l^ay;  for  the  third  bay,  from  r.  and  perp'^ndicular  to  aq,  draw 
1'li  equal  in  length  to  df,  join  A'.s  and  ]cq,  the  bevels  at  .<?  and  q  give  the 
side  cuts  for  all  the  struts  of  the  third  bay.  The  bevel  shown  at  B 
2,  give  the  foot  and  down  cuts  for  the  sides,  if  required,  and  the 
bevels  .shown  at  c  and  8  give  the  foot  and  down  cuts  tor  the  hips;  the 
bevel  shown  at  D  also  give  the  miter  cut  of  sheathing,  and  the  bevel 
shown  at  i  gives  the  cut  on  the  edge.     This  system  of   bevels  for  the 


side  cuts  off  tbe  struts  require  a  set  of  levels  for  every  bay  of  struts. 
A  more  practical  method  is  to  find  the  difference  that  the  wood  is 
less  on  the  back  than  at  the  face,  from  the  thickness  of  the  struts  ; 
then  by  selling  off  the  difference  parallel  to  the  miter  cut,  will  give 
the  cut  for  all.  as  the  difference  for  one  is  the  -same  tor  all.  This 
difference  can  be  easily  obtained  from  the  side  cut  of  the  girts.  As 
some  prefer  to  have  the  lines  for  every  cut,  we  have  thus  described  a 
simple  way  to  obtain  them. 

Figs.  13  and  14.  [Scale  >i"=l ']  Shows  plan  and  elevation 
of  an  Ogee  Octagon  roof  and  ho'du  to  line  off  the  same. 

Fig"  13.  Shows  the  plan  Let  AH,  SD,  AC  and  CI>  indicate 
the  sides  of  a  square;  draw  the  diagonals  BC  and  AD  intersectmg  at 
O;  with  B  for  a  center  and  B  O  for  a  radius,  draw  ark  to  JV,  make  Dili" 
CL,  CJ,  AH,  AG,  Bf  and  BP  equal  i>.V;  join  MN,  JL,  HG 
a'nd/'"P  for  the  sides  of  the  octagon.  I-)raw  the  seat  lines  HN,GM, 
J-jLand  p./"  for  the  hips;  the  seal  of  jacks  may  also  be  drawn  square  lo 
the  walls,  and  sp.iced  as  desired.  Draw  Ji_0  perpendicular  lo  »JH, 
divide  KO  into  any  number  of  parts.  2S,K2,tiH^S  4,  £■<•;  from  the 
points  i,  2,  :i,  4,  t£c.  draw  lines  at  right  angles  lo  KO,  intersecting 
the  seat  line  JIO  at  e.  f,  <f,  h,  d'C. 

Fig.  14.  Shows  the  elevation.  Draw  the  base  line  A'A' parallel  to 
A  H\  make  OA  and  OB  equal  EA  and  EB.  Let  OC  indicate  the  rise 
of  roof  and  C»/ the  amount  to  receive  the  hip-knob  on  one  side;  per- 
pendicular loOCand  through  C  draw  UK  indefinite,  \o\\\JB,  bisect 
J  B  at  X,  bisect  XH  at  n  and*«;  through  m  and  «.draw  a  line  to 
tXA' and  establish  the  point  in;  join  JW.V and  produced  to 
:  W  prolonged  at  K;  then  with  K  for  a  center  and  Kol  as  a 
radius,  draw  the  arc  JN,  again  with  ill  lor  a  centre  and  MN  for  a 
radius  draw  the  arc  XB  for  the  curve  of  the  common  and  jack  ralters; 
the  opposite  side  A,  Z,  Z.  as  shown  may  be  drawn  in  the  same 
manner.  Hoxv  to  determine  the  contour  //,  t,  t,  of  the  hips. 
Make  OA  and  the  spacing  O  7,  7  6",  &€.,  agree  with 
the  line  OK  on  plan;  also  make  CD  and  the  spa- 
cing C  J,  J  i,  'St'c.  agree  with  ihe  seat  O// on  plan.  Make  O/f 
equal  ihe  seat  Oi/ on  plan  Fig.  13;  from  the  points  1,2,3,  &'C. 
erect  perpendiculars  to  XX,  to  intersect  the  curve  of  common  rafter  at 
Z,  Z,  Z,  ^C.\  also  let  fall  perpendiculars  from  the  points  j,  *",  /f,  &=€. 
indefinite  ;  from  the  points  Z,  ^  draw  lines  pirallel  to  XX  and  to 
intersect  the  perpendiculars  at  f,  f,  t,  ^c.\  now  tack  wire  nails  in 
the  points  f.  t,  t,  and  with  the  aid  of  a  pliable  strip  draw  the  curve 
through  the  points  for  the  contour  of  the  hip  r.-fler.  To  find  the 
backing  for  the  hip.  At  -/  on  plan,  the  seat  of  hip  shows  the  thick- 
ness of  hip  squ  red  from  the  ?iigle  J,  take  the  distance  on  one  side 
from  the  point  of  rafter  to  the  wall,  set  this  distance  fmm  /  on  the 
horizontal  lines  fs,  and  with  one  of  the  hip  rafters  slide  the  same  to 
agree  with  the  points  and   scribe  ihnough    them    for  tbe   backing  as 

For  the  length  of  jack  ah  on  plan  Fig. 

1  is  parallel  to  XA'in  elevation;  from  h  on 
iilar  to  XX  to  intersect  the  common  rafter 
,nd  curve  of  jack  to  lis  longest  point.  For 
the  cut  of  jack  against  the  hip.  The  thickness  and  miter  ot  jack 
against  the  hip  on  1  Ian  is  shown,  lines  are  squared  up  from  ihe  miter 
lo  the  top  of  rafter ;  P  shows  the  thickness  and  inclination  of  rafter 
at  that  point,  also  the  bevel  for  the  same. 


shown  by  the  doited  line 
13.    The  jack  «/>  on   plai 
plan  draw  a  line  perpendic 
,IXB  at  r  for  the  length  ? 


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